Joan Birman | Academic Influence

Joan Birman's AcademicInfluence.com Rankings

Joan Birman

Mathematics

#1653

World Rank

#2663

Historical Rank

#674

USA Rank

Topology

#29

World Rank

#46

Historical Rank

#12

USA Rank

Measure Theory

#1113

World Rank

#1427

Historical Rank

#409

USA Rank

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Mathematics

Joan Birman's Degrees

PhD Mathematics University of California, Berkeley
Bachelors Mathematics Barnard College

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Why Is Joan Birman Influential?

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According to Wikipedia, Joan Sylvia Lyttle Birman is an American mathematician, specializing in low-dimensional topology. She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is research professor emerita at Barnard College, Columbia University, where she has been since 1973.

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Joan Birman'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

Braids, Links, and Mapping Class Groups. (1975) (2248)
Knot polynomials and Vassiliev's invariants (1993) (456)
Braids, link polynomials and a new algebra (1989) (432)
A new approach to the word and conjugacy problems in the braid groups (1997) (398)
New points of view in knot theory (1993) (314)
Knotted periodic orbits in dynamical systems—I: Lorenz's equation (1983) (304)
Braids, Links, and Mapping Class Groups. (AM-82) (1975) (304)
Abelian and solvable subgroups of the mapping class groups (1983) (257)
Mapping class groups and their relationship to braid groups (1969) (227)
On the Mapping Class Group of Closed Surfaces as Covering Spaces (1971) (156)
Braids (2021) (152)
Braids: A Survey (2004) (151)
Isotopies of homeomorphisms of Riemann surfaces and a theorem about Artin's braid group (1972) (150)
Studying links via closed braids. III. Classifying links which are closed 3-braids (1993) (129)
Geodesics with bounded intersection number on surfaces are sparsely distributed (1985) (110)
Seifert and Threlfall : a textbook of topology . Seifert : topology of 3-dimensional fibered spaces (1980) (101)
On Siegel's modular group (1971) (90)
On braid groups (1969) (83)
STUDYING LINKS VIA CLOSED BRAIDS I (1992) (81)
Heegaard splittings of branched coverings of (1975) (81)
The -invariant of 3-manifolds and certain structural properties of the group of homeomorphisms of a closed, oriented 2-manifold (1978) (77)
Studying links via closed braids. V. The unlink (1992) (77)
On the homeotopy group of a non-orientable surface (1972) (73)
On the Jones polynomial of closed 3-braids (1985) (71)
Conjugacy in Garside groups I: cyclings, powers and rigidity (2006) (71)
Stabilization in the braid groups II: Transversal simplicity of knots (2003) (70)
Studying links via closed braids IV: composite links and split links (1990) (69)
An Algorithm for Simple Curves on Surfaces (1984) (67)
The Infimum, Supremum, and Geodesic Length of a Braid Conjugacy Class (2000) (67)
An inverse function theorem for free groups (1973) (61)
Special positions for essential Tori in link complements (1994) (59)
STUDYING LINKS VIA CLOSED BRAIDS I: A FINITENESS THEOREM (1992) (57)
Conjugacy in Garside groups III: Periodic braids (2006) (56)
A new twist on Lorenz links (2007) (54)
On transversally simple knots (1999) (52)
On the Stable Equivalence of Plat Representations of Knots and Links (1976) (51)
STUDYING SURFACES VIA CLOSED BRAIDS (1998) (50)
Conjugacy in Garside groups II: structure of the ultra summit set (2006) (49)
Studying links via closed braids II: On a theorem of Bennequin (1991) (47)
Stabilization in the braid groups I: MTWS (2003) (46)
STABILIZATION IN THE BRAID GROUPS (2002) (46)
A new algorithm for recognizing the unknot (1998) (45)
Heegaard splittings of prime $3$-manifolds are not unique. (1976) (44)
DEHN’S ALGORITHM REVISITED, WITH APPLICATIONS TO SIMPLE CURVES ON SURFACES (1987) (40)
Braids, links, and mapping class groups : based on lecture notes by James Cannon (1975) (40)
Lifting and projecting homeomorphisms (1972) (38)
One-Sided Heegaard Splittings and Homeotopy Groups of Some 3-Manifolds (1984) (37)
Mapping class groups of surfaces (1988) (34)
STUDYING LINKS VIA CLOSED BRAIDS VI : A NON-FINITENESS THEOREM (1992) (33)
The homeomorphism problem for $S^3$ (1973) (30)
3-fold branched coverings and the mapping class group of a surface (1985) (30)
A note on closed 3-braids (2008) (28)
ON THE EQUIVALENCE OF HEEGAARD SPLITTINGS OF CLOSED, ORIENT ABLE 3-MANIFOLDS (1975) (25)
Jones’ braid-plat formula and a new surgery triple (1988) (20)
Automorphisms of the fundamental group of a closed, orientable 2-manifold (1969) (20)
Errata: Presentations of the mapping class group (1994) (19)
Fixed points of pseudo-Anosov diffeomorphisms of surfaces (1982) (17)
Markov classes in certain finite quotients of artin’s braid group (1986) (17)
Efficient geodesics and an effective algorithm for distance in the complex of curves (2014) (16)
Abelian quotients of the mapping class group of a 2-manifold (1970) (16)
Erratum to `Isotopies of homeomorphisms of Riemann surfaces’ (2017) (16)
Finite-Dimensional Representations of Artin's Braid Group (1994) (15)
Scientific Publishing: A Mathematician's Viewpoint (2000) (15)
Holonomic and Legendrian parametrizations of knots (1998) (14)
Review: F. M. Goodman, P. de la Harpe, and V. F. R. Jones, Coxeter graphs and towers of algebras (1991) (13)
Recent developments in braid and link theory (1991) (13)
MAPPING CLASS GROUPS OF SURFACES: A SURVEY (1974) (12)
SPECIAL REPRESENTATIONS FOR 3-MANIFOLDS (1979) (12)
Poincare's conjecture and the homeotopy group of a closed, orientable 2-manifold (1974) (12)
The topology of 3-manifolds, Heegaard distance and the mapping class group of a 2-manifold (2005) (12)
A representation theorem for fibered knots and their monodromy maps (1979) (11)
On the Singular Braid Monoid (2003) (11)
TOWARDS AN IMPLEMENTATION OF THE B–H ALGORITHM FOR RECOGNIZING THE UNKNOT (2001) (11)
Algorithms in the surface mapping class groups (1997) (10)
ALGEBRAIC LINEARITY FOR AN AUTOMORPHISM OF A SURFACE GROUP (1988) (10)
Finite rigid sets and homologically non-trivial spheres in the curve complex of a surface (2013) (9)
Cubulations mod bubble moves (9)
A normal form in the homeotopy group of a surface of genus 2, with applications to 3-manifolds (1972) (8)
Studying links via closed braids IV: composite links and split links (1990) (8)
POLYNOMIAL INVARIANTS OF PSEUDO-ANOSOV MAPS (2010) (8)
The curve complex has dead ends (2012) (8)
The mathematical legacy of Wilhelm Magnus : groups, geometry, and special functions : Conference on the Legacy of Wilhelm Magnus, May 1-3, 1992, Polytechnic University, Brooklyn, New York (1994) (8)
ON MARKOV'S THEOREM (2002) (8)
Plat presentations for link groups (1973) (7)
On minimal Heegaard splittings. (1980) (7)
Braided chord diagrams (1998) (7)
ON THE COMBINATORICS OF VASSILIEV INVARIANTS (1994) (7)
Knots, braids, and mapping class groups -- papers dedicated to Joan S. Birman : proceedings of a conference in low dimensional topology in honor of Joan S. Birman's 70th birthday, March 14-15, 1998, Columbia University, New York, New York (2001) (6)
Braids : proceedings of the AMS-IMS-SIAM joint summer research conference on Artin's braid group held July 13-26, 1986 at the University of California, Santa Cruz, California (1988) (6)
Non‐conjugate braids can define isotopic knots (1969) (6)
Special Heegaard splittings for closed, oriented 3-manifolds (1978) (6)
A calculus on links in the 3-sphere (1992) (5)
Stabilization in the Braid Groups (with applications to transverse knots) (2002) (5)
A note on transversal knots which are closed 3-braids (2007) (4)
THE WORK OF VAUGHAN F. R. JONES (1997) (4)
Calculating the image of the second Johnson-Morita representation (2007) (3)
The mathematics of Lorenz knots (2013) (3)
On Finite Type Invariants of Links and Rational Homology Spheres Derived from the Jones Polynomial and Witten-Reshetikhin-Turaev Invariant (1996) (3)
Erratum: Special positions for essential tori in link complements (Topology 33 (3) (1994) pp. 525–556) (1998) (3)
G T ] 2 9 Ju n 20 10 A polynomial invariant of pseudo-Anosov maps (2010) (3)
PA mapping classes with minimum dilatation and Lanneau-Thiffeault polynomials (2011) (3)
BRAIDS, KNOTS AND CONTACT STRUCTURES (2004) (3)
Errata: On the Conjugacy Problem in the Braid Group (1982) (2)
On pseudo-Anosov mapping classes with minimum dilatation and Lanneau-Thiffeault numbers (2011) (2)
Obstructions to trivializing a knot (2002) (2)
A note on the construction of simply-connected 3-manifolds as branched covering spaces of ³ (1976) (1)
G T ] 2 2 Fe b 20 07 Conjugacy in Garside Groups III : Periodic braids (2008) (1)
Memories of Vaughan Jones (2021) (1)
Correction to „discriminant and projective invariants of binary forms”︁ C.P.A.M., Vol. XXIII, 1970, pp. 269‐275 (1973) (1)
Discriminant and projective invariants of binary forms (1970) (1)
Book Review: Braid groups (With the graphical assistance of Olivier Dodane); Ordering braids (2011) (1)
On the Burau representation of B4 (2021) (1)
Lorenz knots, T-links and twisted torus links (2007) (1)
Distance and intersection number in the curve graph of a surface (2018) (1)
CHAPTER 2. BRAIDS AND LINKS (1975) (1)
A note on transversal knots that are closed 3-braids (2007) (1)
Holonomic parametrizations of knots (1998) (1)
BIRS workshop on braid groups and applications (0)
CHAPTER 5. PLATS AND LINKS (1975) (0)
Distance and intersection number in C ( S ) Birman , Morse , Wrinkle (2018) (0)
Review: Gerhard Burde and Heiner Zieschang, Knots, and Louis H. Kauffman, On knots (1988) (0)
O ct 2 02 2 Algebra , Topology and the discoveries of (2022) (0)
A Note on Closed 3-braids * Dedicated to the Memory of Xiao-song Lin (2008) (0)
APPENDIX: RESEARCH PROBLEMS (1975) (0)
1 8 Fe b 20 02 On Markov ’ s Theorem (2008) (0)
Symplectic Heegaard splittings and linked abelian groups (2007) (0)
A new look at the word problem in the braid group (1997) (0)
IE y-I OF 3-OLDS CERTAIN STRUCIIJRAL PROPERTIES OF THE GROUP OF HO1\vIEOMORPHISMS OF A CLOSED, ORIENTED 2-MANIFOLD (2016) (0)
G T ] 3 M ar 1 99 9 A NEW ALGORITHM FOR RECOGNIZING THE UNKNOT (2008) (0)
CHAPTER 3. MAGNUS REPRESENTATIONS (1975) (0)
Women's History Month (2013) (0)
The braid groups, knots and algebraic geometry (1997) (0)
Characteristic polynomials of pseudo-Anosov maps (2010) (0)
Efficient geodesics and an effective algorithm for distance in the complex of curves (2016) (0)
Book Review: On knots (1988) (0)
The curve complex has dead ends (2014) (0)
Se p 20 03 To appear in the Handbook of Knot Theory (2008) (0)
CHAPTER 4. MAPPING CLASS GROUPS (1975) (0)
The Mathematics of Joan Birman Dan Margalit (2019) (0)
2 6 Ju n 20 02 OBSTRUCTIONS TO TRIVIALIZING A KNOT (2002) (0)
Knot Theory. By Charles Livingston (1995) (0)
Table of Contents for the Handbook of Knot Theory (2003) (0)
On the $\mu$-invariant of $Z$-homology 3-spheres (1976) (0)
CHAPTER 1. BRAID GROUPS (1975) (0)
1 0 A pr 2 01 4 The curve complex has dead ends (0)
ON THE /^-INVARIANT OF Z-HOMOLOGY 3-SPHERES (2007) (0)
On the Burau representation of $B_3$ (2022) (0)
A new look at knot polynomials (1992) (0)
ON JONES KNOT INVARIANTS AND VASSILIEV INVARIANTS (0)
Letters to the editor (0)
A pr 2 00 1 On transversally simple knots (1999) (0)
G T ] 2 1 Se p 20 06 Conjugacy in Garside Groups III : Periodic braids (2008) (0)

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