Armand Borel | Academic Influence

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Armand Borel

Mathematics

#59

World Rank

#179

Historical Rank

Measure Theory

#51

World Rank

#87

Historical Rank

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Mathematics

Armand Borel's Degrees

PhD Mathematics University of Geneva

Why Is Armand Borel Influential?

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According to Wikipedia, Armand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups.

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Armand Borel's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Linear Algebraic Groups (1991) (1393)
Sur La Cohomologie des Espaces Fibres Principaux et des Espaces Homogenes de Groupes de Lie Compacts (1953) (1095)
Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups (1999) (986)
CHARACTERISTIC CLASSES AND HOMOGENEOUS SPACES, I.* (1958) (888)
Arithmetic subgroups of algebraic groups (1961) (782)
Seminar on Transformation Groups. (1961) (698)
Automorphic Forms, Representations, and L-Functions (1979) (693)
Seminar on Algebraic Groups and Related Finite Groups (1970) (691)
Compactification of Arithmetic Quotients of Bounded Symmetric Domains (1966) (689)
Reductive groups over local fields (1979) (688)
Stable real cohomology of arithmetic groups (1974) (673)
Corners and arithmetic groups (1973) (612)
Groupes Réductifs (1965) (580)
Introduction aux groupes arithmétiques (1969) (554)
Algebraic D-modules (1987) (473)
Compact Clifford-Klein forms of symmetric spaces (1963) (470)
Les sous-groupes fermés de rang maximum des groupes de Lie clos (1949) (449)
Homomorphismes "abstraits" de groupes algébriques simples (1973) (344)
Admissible representations of a semi-simple group over a local field with vectors fixed under an iwahori subgroup (1976) (292)
Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I (1971) (267)
Kählerian Coset Spaces of Semisimple Lie Groups. (1954) (264)
Théorèmes de finitude en cohomologie galoisienne (1964) (260)
La classe d'homologie fondamentale d'un espace analytique (1961) (251)
Commensurability classes and volumes of hyperbolic 3-manifolds (1981) (247)
Some finiteness properties of adele groups over number fields (1963) (238)
Compléments À L’Article: «Groupes Réductifs» (1972) (237)
Compactifications of Symmetric and Locally Symmetric Spaces (2005) (233)
Properties and linear representations of Chevalley groups (1970) (222)
Algebraic groups and discontinuous subgroups (1966) (221)
Density Properties for Certain Subgroups of Semi-Simple Groups Without Compact Components (1960) (211)
Homology theory for locally compact spaces. (1960) (207)
Le théorème de Riemann-Roch (1958) (205)
Some metric properties of arithmetic quotients of symmetric spaces (1970) (194)
Groupes de Lie et Puissances Reduites de Steenrod (1953) (183)
Sur L'Homologie et la Cohomologie des Groupes de Lie Compacts Connexes (1954) (173)
Compactifications of Symmetric Spaces (1998) (172)
Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes (1961) (170)
Some remarks about Lie groups transitive on spheres and tori (1949) (160)
Groupes Lineaires Algebriques (1956) (157)
Density and maximality of arithmetic subgroups. (1966) (148)
Topology of Lie groups and characteristic classes (1955) (144)
Almost commuting elements in compact Lie groups (1999) (143)
La cohomologie mod 2 de certains espaces homogènes (1953) (142)
Topics in the Homology Theory of Fibre Bundles (1967) (140)
Cohomologie de SLn et valeurs de fonctions z^eta aux points entiers (1977) (139)
Cohomologie d'immeubles et de groupes s-arithmétiques (1976) (132)
Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups (1989) (126)
On Semi-Simple Automorphisms of Lie Algebras (1955) (103)
Existence of discrete cocompact subgroups of reductive groups over local fields. (1978) (101)
Essays in the history of Lie groups and algebraic groups (2001) (98)
$L^2$-cohomology of locally symmetric manifolds of finite volume (1983) (95)
Sur certains sous-groupes des groupes de Lie compacts (1953) (83)
Seminar on transformation groups (AM-46) (1961) (80)
LAPLACIAN AND THE DISCRETE SPECTRUM OF AN ARITHMETIC GROUP (1983) (75)
Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn (1994) (73)
Classification of algebraic semi-simple groups (1966) (69)
On the Curvature Tensor of the Hermitian Symmetric Manifolds (1960) (69)
Semisimple groups and Riemannian symmetric spaces (1998) (69)
Automorphic Forms on Sl2 (R) (1997) (65)
Les Bouts Des Espaces Homogenes de Groupes De Lie (1953) (55)
The L^2-cohomology of negatively curved Riemannian symmetric spaces (1985) (54)
Mathematics: art and science (1983) (53)
Automorphic forms and automorphic representations (1979) (51)
Introduction to automorphic forms (1966) (49)
Regularization theorems in Lie algebra cohomology. Applications (1983) (47)
On the cuspidal cohomology of $S$-arithmetic subgroups of reductive groups over number fields (1996) (46)
Compactifications of Locally Symmetric Spaces (2006) (46)
Values of isotropic quadratic forms at $S$-integral points (1992) (43)
Responses to: A. Jaffe and F. Quinn, “Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics” [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1–13; MR1202292 (94h:00007)] (1994) (43)
Injective endomorphisms of algebraic varieties (1969) (42)
Uniqueness conditions for certain holomorphic mappings (1967) (41)
Représentations de groupes localement compacts (1972) (40)
Sous-groupes épimorphiques de groupes linéaires algébriques II (1992) (39)
Automorphic forms on SL[2](R) (2008) (39)
The Rank Conjecture For Number Fields (1994) (38)
The Poincaré duality in generalized manifolds. (1957) (36)
Seminar on Complex Multiplication (2009) (33)
On the compactification of arithmetically defined quotients of bounded symmetric domains (1964) (30)
Automorphic Forms, Representations and -Functions, Part 2 (1979) (28)
Sheaf Theoretic Intersection Cohomology (1984) (26)
Théorèmes de structure et de conjugaison pour les groupes algébriques linéaires (1978) (26)
On affine algebraic homogeneous spaces (1985) (24)
Les fonction automorphes de plusieurs variables complexes (1952) (23)
Values of indefinite quadratic forms at integral points and flows on spaces of lattices (1995) (23)
Homology and Cohomology of Compact Connected Lie Groups. (1953) (23)
Oeuvres - Collected Papers IV (2001) (21)
Class Functions, Conjugacy Classes and Commutators in Semisimple Lie Groups (2001) (21)
Reduction Theory for Arithmetic Groups (1966) (20)
Generalized modular symbols (1990) (20)
The School of Mathematics at the Institute for Advanced Study (2001) (19)
Cohomologie de certains groupes discrets et laplacien $p$-adique (1974) (18)
Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups (1990) (17)
AUTOMORPHIC FORMS ON REDUCTIVE GROUPS (2002) (17)
Rationally connected homogeneous spaces (1996) (17)
Nouvelle démonstration d’un théorème de P. A. Smith (1955) (17)
Symmetric compact complex spaces (1979) (16)
Commutative subgroups and torsion in compact Lie groups (1960) (16)
Stable and $L^2$-cohomology of arithmetic groups (1980) (16)
Cohomologie des espaces localement compacts d'après J. Leray (1964) (15)
Cohomologie des espaces localement compacts (1964) (15)
Sous-groupes compacts maximaux des groupes de Lie (1951) (15)
Continuous and differentiable cohomology for locally compact totally disconnected groups (2000) (15)
Hermann Weyl and Lie Groups (2001) (14)
L 2 -Cohomology and Intersection Cohomology of Certain Arithmetic Varieties (1983) (14)
Twenty-Five Years with Nicolas Bourbaki, 1949-1973 (1998) (13)
Cohomology and Spectrum of an Arithmetic Group (2001) (13)
Representations of Reductive Groups (1980) (13)
On Free Subgroups of Semi-simple Groups (2001) (13)
Some properties of adele groups attached to algebraic groups (1961) (11)
A vanishing theorem in relative Lie algebra cohomology (1987) (11)
Formes automorphes et séries de dirichlet (1976) (10)
Algebraic groups and arithmetic groups (2006) (10)
Cohomologie de certains groupes discretes et lapiacien p-adique [d'après H. Garland] (1975) (10)
Seminar on complex multiplication : seminar held at the Institute for Advanced Study, Princeton, N.J., 1957-58 : [papers] (1966) (10)
Œuvres = Collected papers (1983) (10)
Pseudo-concavité et groupes arithmétiques (1970) (10)
Cohomologie d’intersection et L 2-cohomologie de variétés arithmétiques de rang rationnel 2 (2001) (9)
Hermann Weyl, 1885-1985 : centenary lectures (1986) (9)
Groupes d'homotopie des groupes de Lie, I (1950) (9)
Errata-Corrigé : «Cohomologie de $SL_n$ et valeurs de fonctions zêta aux points entiers» (1980) (7)
Les espaces hermitiens symétriques (1954) (7)
Introduction to Middle Intersection Cohomology and Perverse Sheaves (2001) (7)
On the set of discrete subgroups of bounded covolume in a semisimple group (1987) (6)
Emmy Noether in Bryn Mawr : proceedings of a symposium (1983) (6)
Values of Zeta-Functions at Integers, Cohomology and Polylogarithms (2001) (6)
Introduction to the Cohomology of Arithmetic Groups (2004) (6)
From PL to Sheaf Theory (Rock to Bach) (1984) (6)
Automorphic forms on SL2(ℝ): Analytic continuation of the Eisenstein series (1997) (5)
Henri Poincaré and Special Relativity (2001) (4)
Fixed points of elementary commutative groups (1959) (3)
Correction and complement to the paper Regularization theorems in Lie algebra cohomology. Applications. (1990) (3)
The Work of Chevalley in Lie Groups and Algebraic Groups (2001) (3)
Sous-groupes discrets de groupes semi-simples (1971) (3)
TRANSFORMATION GROUPS WITH TWO CLASSES OF ORBITS. (1957) (3)
On the Place of Mathematics in Culture (1994) (3)
Valeurs de formes quadratiques aux points entiers (2001) (3)
Riemannian Symmetric Spaces (1998) (3)
Opérateurs de Hecke et fonctions zêta (1966) (3)
Automorphic forms on SL2(ℝ): Contents (1997) (3)
Jean Leray and Algebraic Topology (2001) (3)
The homological properties of H-spaces (1967) (2)
CHAPTER XIII: FIXED POINT THEOREMS FOR ELEMENTARY COMMUTATIVE GROUPS II (1961) (2)
Borel Subgroups; Reductive Groups (1991) (2)
Travaux de Mostow sur les espaces homogènes (1956) (2)
Background Material from Algebraic Geometry (1991) (2)
Lie Groups and Linear Algebraic Groups I . Complex and Real Groups (2001) (2)
On the development of lie group theory (1980) (2)
Groupes réductifs sur un corps local, 1, Données radicielles valuées . Compléments a l'article : "Groupes réductifs" (1972) (1)
Some Recollections of Harish-Chandra (2001) (1)
Le theoreme fondamental (1964) (1)
Topology and fixed point theorems = Topologie et théorème du point fixe (1998) (1)
Algebraic Groups and Galois Theory in the Work of Ellis R. Kolchin (2001) (1)
La pensée magique dans l'art (1987) (1)
Deane Montgomery (1909 −1992) (2001) (1)
Groupes localement compacts (1951) (1)
Maximal Compact Subgroups of Lie Groups (1998) (1)
CHAPTER II: HOMOLOGY AND DUALITY IN GENERALIZED MANIFOLDS (1961) (0)
Class invariants II (1966) (0)
Automorphic forms on SL2(ℝ): References (1997) (0)
The computation of certain cohomology groups (2000) (0)
Non-cocompact -arithmetic subgroups (2000) (0)
Collected papers of topology (1950) (0)
Automorphic forms on SL2(ℝ): Preface (1997) (0)
Automorphic forms on SL2(ℝ): Definition and convergence of Eisenstein series (1997) (0)
CHAPTER I. STATEMENT OF THE THEOREM OUTLINE OF THE PROOF (1965) (0)
[Ametropia and occupations in Building and Public Works]. (1980) (0)
African and European children, Elim, Limpopo, South Africa, ca. 1896-1911 (2012) (0)
Cohomology with respect to an induced representation (2000) (0)
[Venereal tumors of the dog (Sticker sarcoma); experimental radiobiology]. (1952) (0)
[Pithiatic behavior and spontaneous abortion following typhoid encephalitis; third pregnancy managed at term by endocrine therapy]. (1952) (0)
André Weil: quelques souvenirs (2001) (0)
Differentiable cohomology for products of real Lie groups and T.D. groups (2000) (0)
Cohomology of discrete subgroups and Lie algebra cohomology (2000) (0)
Réponse à la remise du prix Balzan 1992 (2001) (0)
CHAPTER V: THE ACTION OF Zp T1 : LOCAL THEOREMS (1961) (0)
Algebre spectrale des espaces fibres (1964) (0)
Cohomology of discrete cocompact subgroups (2000) (0)
Automorphic forms on SL2(ℝ): Poincaré series (1997) (0)
Representations of G (1997) (0)
Notations. Formulaire de convolution (1972) (0)
Spectral sequence of a fibre bundle (1967) (0)
Quelques Notions Et Résultats De Base (1972) (0)
Automorphic forms on SL2(ℝ): Introduction (1997) (0)
Automorphic forms on SL2(ℝ): Convolution operators on cuspidal functions (1997) (0)
On the Work of E. Cartan on Real Simple Lie Algebras (2001) (0)
Automorphic forms on SL2(ℝ): Prerequisites and notation (1997) (0)
Sous-groupes discrets de groupes p-adiques à covolume borné (2001) (0)
Invariant eigendistributions on a semisimple lie algebra . Groupes réductifs (1965) (0)
CHAPTER I: COHOMOLOGY MANIFOLDS (1961) (0)
Scalar product, Laplacian and Casimir element (2000) (0)
ANNALES SCIENTIFIQUES DE L'É.N.S. (1974) (0)
Élie Cartan, symmetric spaces and Lie groups (2001) (0)
André Weil and Algebraic Topology (2001) (0)
Applications aux espaces fibres (1964) (0)
Automorphic forms on SL2(ℝ): Constant term: the fundamental estimate (1997) (0)
Quelques réflexions sur les mathématiques en général et la théorie des groupes en particulier (2001) (0)
Cohomology mod 2 of some homogeneous spaces (2012) (0)
Discours prononcee n seance publique le 30 septembre 2003 en hommage (2004) (0)
CHAPTER XVI: REMARKS ON THE SPECTRAL SEQUENCE OF A MAP (1961) (0)
The unit disc model (1997) (0)
La Série Discrète (Résultats; bouts de démonstrations) (1972) (0)
Full Reducibility and Invariants for SL2(C) (2001) (0)
Linear algebraic groups in the 19th century (2001) (0)
The Langlands classification and uniformly bounded representations (2000) (0)
Cohomologie et rigidité d'espaces compacts localement symétriques (1964) (0)
Notation and preliminaries (2000) (0)
CHAPTER XIV: ONE OR W O CLASSES OF ORBITS (1961) (0)
Automorphic Forms on SL2 (R): Review of SL2(ℝ), differential operators, and convolution (1997) (0)
CHAPTER IV: THE ACTION OF Zp OR T1 : GLOBAL THEOREMS (1961) (0)
Classifying spaces of the classical groups (1967) (0)
Automorphic forms on SL2(ℝ): Spectral decomposition of L 2(Γ\ G ): the discrete spectrum (1997) (0)
Twenty-Five Years with Nicolas Bourbaki , 1949 – 1973 Armand Borel (1998) (0)
Automorphic forms on SL2(ℝ): Finite dimensionality of the space of automorphic forms of a given type (1997) (0)
Orthogonal Involutive Lie Algebras (1998) (0)
TABLE OP CONTENTS (1961) (0)
Automorphic forms on SL2(ℝ): Spectral decomposition of L 2(Γ\ G ) m with respect to C (1997) (0)
On cohomology of principal fiber bundles and homogeneous spaces of compact Lie groups (2012) (0)
Locally Symmetric Spaces (1998) (0)
Continuous cohomology and differentiable cohomology (2000) (0)
Full reducibility and invariants for ₂(ℂ) (2001) (0)
Automorphic forms on SL2(ℝ): Spectral decomposition of L 2(Γ\ G ): the continuous spectrum (1997) (0)
Linear algebraic groups in the 20th century (2001) (0)
Cohomology with coefficients in Π_ (2000) (0)
General Notions Associated With Algebraic Groups (1991) (0)
Hermitian Symmetric Spaces (1998) (0)
Armand Borel : a great mathematician of the twentieth century (2006) (0)
Automorphic forms on SL2(ℝ): Action of G on X. Discrete subgroups of G . Reduction theory (1997) (0)
SPECIAL PROGRAM IN GROUP THEORY. (1970) (0)
On the Selection of the Invited Speakers to the 1978 ICM (1979) (0)
Values of Quadratic Forms at S -integral points (2001) (0)
Cohomology with coefficients in Π_{∞}(): The -adic case (2000) (0)
P-adic linear groups with ergodic automorphisms (1976) (0)
Compact Groups, Klein Forms of Symmetric Spaces (1998) (0)
Automorphic forms on SL2(ℝ): Generalities on representations of G (1997) (0)
CHAPTER X: THE SPECTRAL SEQUENCE OF A BIFILTERED MODULE, (1961) (0)
The construction of certain unitary representations and the computation of the corresponding cohomology groups (2000) (0)
CHAPTER XI: THE SPECTRAL SEQUENCE OF FARY (1961) (0)
Automorphic forms on SL2(ℝ): Growth conditions. Automorphic forms (1997) (0)
Applications et complements (1964) (0)
Reviews (2001) (0)
Relative Lie algebra cohomology (2000) (0)
GENERALIZED MODULAR SYMBOLS AND COHOMOLOGY OF ARITHMETIC GROUPS(WORKSHOP ON ALGEBRAIC GROUPS AND RELATED TOPICS) (1990) (0)
Automorphic forms on SL2(ℝ): Eisenstein series and automorphic forms orthogonal to cusp forms (1997) (0)

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