Peter Shalen

Q: What Schools Are Affiliated With Peter Shalen

Peter Shalen is affiliated with the following schools: Columbia University, University of Illinois Chicago, Harvard University, Rice University, University of California, Berkeley, University of Chicago

Peter Shalen's AcademicInfluence.com Rankings

Peter Shalen

Mathematics

#1709

World Rank

#2742

Historical Rank

#699

USA Rank

Measure Theory

#3230

World Rank

#3819

Historical Rank

#935

USA Rank

mathematics Degrees

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Mathematics

Peter Shalen's Degrees

PhD Mathematics University of California, Berkeley

Why Is Peter Shalen Influential?

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According to Wikipedia, Peter B. Shalen is an American mathematician, working primarily in low-dimensional topology. He is the "S" in JSJ decomposition. Life He graduated from Stuyvesant High School in 1962, and went on to earn a B.A. from Harvard College in 1966 and his Ph.D. from Harvard University in 1972. After posts at Columbia University, Rice University, and the Courant Institute, he joined the faculty of the University of Illinois at Chicago.

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Peter Shalen'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

Varieties of group representations and splittings of 3-manifolds (1983) (689)
Seifert fibered spaces in 3-manifolds (1979) (671)
Valuations, Trees, and Degenerations of Hyperbolic Structures, I (1984) (406)
Plane curves associated to character varieties of 3-manifolds (1994) (400)
Dehn surgery on knots (1985) (312)
Degenerations of hyperbolic structures, III: Actions of 3-manifold groups on trees and Thurston’s compactness theorem (1988) (106)
Seifert fibered spaces in irreducible, sufficiently-large 3-manifolds (1976) (105)
Degenerations of hyperbolic structures, II: Measured laminations in 3-manifolds (1988) (98)
Bounded, separating, incompressible surfaces in knot manifolds (1984) (86)
Dendrology of Groups: An Introduction (1987) (80)
Generalized triangle groups (1987) (76)
Free actions of surface groups on R-trees (1991) (69)
Paradoxical decompositions, 2-generator Kleinian groups, and volumes of hyperbolic 3-manifolds (1992) (64)
Free Kleinian groups and volumes of hyperbolic {3}-manifolds (1996) (61)
Real-analytic actions of lattices (1999) (53)
Growth rates, _{}-homology, and volumes of hyperbolic 3-manifolds (1992) (50)
Linear groups of finite cohomological dimension (1981) (41)
Dendrology of groups in low ${\bf Q}$-ranks (1990) (37)
Linear representations of certain amalgamated products (1979) (34)
Volumes of hyperbolic Haken manifolds, I (1994) (33)
Dehn surgery, homology and hyperbolic volume (2005) (30)
Singular surfaces, mod 2 homology, and hyperbolic volume, I (2005) (28)
Amalgamated products and finitely presented groups (1990) (27)
Approximation by Maximal Cusps in Boundaries of Deformation Spaces of Kleinian Groups (2003) (27)
Three-manifolds and Baumslag–Solitar groups (2001) (25)
Surface homeomorphisms and periodicity (1977) (24)
Groups of real-analytic diffeomorphisms of the circle (2002) (23)
Groups whose three-generator subgroups are free (1989) (23)
The first betti number of the smallest closed hyperbolic 3-manifold (1998) (20)
Hyperbolic volume, Heegaard genus and ranks of groups (2009) (19)
Peripheral structure of 3-manifolds (1976) (19)
Boundary slopes of knots (1999) (19)
On Ahlfors' finiteness theorem (1989) (17)
4‐free groups and hyperbolic geometry (2008) (16)
INFINITELY DIVISIBLE ELEMENTS IN 3-MANIFOLD GROUPS (1975) (14)
Characteristic subsurfaces and Dehn filling (2002) (13)
An introduction to compactifying spaces of hyperbolic structures by actions on trees (1985) (12)
Margulis numbers for Haken manifolds (2010) (12)
The volume of a hyperbolic 3-manifold with Betti number 2 (1994) (11)
Hyperbolic volume and modp homology (1993) (10)
A Generic Margulis Number for Hyperbolic 3-Manifolds (2010) (10)
Lattice actions, 3-manifolds and homology (2000) (10)
A torus theorem for regular branched covers of $S^3$. (1981) (9)
Real-analytic, volume-preserving actions of lattices on 4-manifolds (2002) (8)
Affine Algebraic Sets and Some Infinite Finitely Presented Groups (1987) (8)
Knots with only two strict essential surfaces (2004) (8)
A “piecewise-linear” method for triangulating 3-manifolds (1984) (8)
Chapter IV The Proof in the Case of No Incompressible Surface (1984) (8)
Homeomorphic graph manifolds: A contribution to the μ constant problem (1999) (8)
Characteristic subsurfaces, character varieties and Dehn fillings (2006) (7)
Correction to: “Dehn surgery on knots” (1988) (7)
Small optimal Margulis numbers force upper volume bounds (2010) (6)
Volume and topology of bounded and closed hyperbolic 3-manifolds (2009) (6)
Dendrology and its applications (2011) (6)
Volume and homology of one-cusped hyperbolic 3-manifolds (2007) (5)
Incompressible surfaces, hyperbolic volume, Heegaard genus and homology (2008) (5)
Separating, incompressible surfaces in 3-manifolds (1979) (5)
The diameter of the set of boundary slopes of a knot (2004) (4)
Betti numbers and injectivity radii (2009) (4)
Simplicial approximation and low-rank trees (1991) (4)
VOLUMES OF HYPERBOLIC HAKEN MANIFOLDS, II (1997) (3)
A remark on finitely presented infinite-dimensional algebras (1990) (2)
The geometry of k-free hyperbolic 3-manifolds (2018) (2)
Orders of elements in finite quotients of Kleinian groups (2011) (2)
Heegaard genus and ranks of groups P (2008) (1)
-HOMOLOGY, AND VOLUMES OF HYPERBOLIC 3-MANIFOLDS (2009) (1)
Homology and volume of hyperbolic $3$-orbifolds, and enumeration of arithmetic groups (2015) (1)
Heegaard genus and ranks of groups P (2008) (1)
Euler characteristics, free subgroups, and lengths of loops in hyperbolic 3-manifolds (2023) (1)
The ratio of homology rank to hyperbolic volume, II (2021) (1)
Margulis numbers and number fields (2009) (0)
Margulis numbers for Haken manifolds (2011) (0)
Cohomological dimension of groups acting on ℝ-trees (1991) (0)
Volume and Homology for Hyperbolic $3$-Orbifolds, I (2017) (0)
G T ] 2 2 N ov 2 00 6 CHARACTERISTIC SUBSURFACES , CHARACTER VARIETIES AND DEHN FILLINGS (0)
N ov 2 00 2 Characteristic subsurfaces and Dehn filling (2008) (0)
Volumes of 5-free hyperbolic 3-manifolds. (2020) (0)
KNOTS , LINKS AND REPRESENTATION SHIFTS (2003) (0)
GROWTH RATES , 1 P-HOMOLOGY , AND VOLUMES OF HYPERBOLIC 3-MANIFOLDS (2009) (0)
Topology Proceedings 54 (2018) pp. 49-68: On Periodic Data of Diffeomorphisms with One Saddle Orbit (2008) (0)

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What Schools Are Affiliated With Peter Shalen?

Peter Shalen is affiliated with the following schools:

Peter Shalen's Academic­Influence.com Rankings