Robion Kirby | Academic Influence

Robion Kirby's AcademicInfluence.com Rankings

Robion Kirby

Mathematics

#352

World Rank

#732

Historical Rank

#168

USA Rank

Algebraic Geometry

#152

World Rank

#159

Historical Rank

#38

USA Rank

Number Theory

#192

World Rank

#249

Historical Rank

#37

USA Rank

Measure Theory

#1552

World Rank

#1926

Historical Rank

#517

USA Rank

mathematics Degrees

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Mathematics

Robion Kirby's Degrees

PhD Mathematics University of California, Berkeley
Masters Mathematics University of California, Berkeley
Bachelors Mathematics University of California, Berkeley

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Why Is Robion Kirby Influential?

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According to Wikipedia, Robion Cromwell Kirby is a Professor of Mathematics at the University of California, Berkeley who specializes in low-dimensional topology. Together with Laurent C. Siebenmann he developed the Kirby–Siebenmann invariant for classifying the piecewise linear structuress on a topological manifold. He also proved the fundamental result on the Kirby calculus, a method for describing 3-manifolds and smooth 4-manifolds by surgery on framed links. Along with his significant mathematical contributions, he has over 50 doctoral students and is the editor of an influential problem list.

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Robion Kirby'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

Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (1977) (634)
A calculus for framed links inS3 (1978) (467)
The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl(2, C) (1991) (379)
Deformations of Spaces of Imbeddings (1971) (247)
On the triangulation of manifolds and the Hauptvermutung (1969) (230)
The topology of 4-manifolds (1989) (178)
Stable homeomorphisms and the annulus conjecture (1969) (151)
Branched covers of surfaces in 4-manifolds (1980) (132)
Trisecting 4–manifolds (2012) (129)
Pin structures on low-dimensional manifolds (1991) (110)
Dedekind sums, μ-invariants and the signature cocycle (1994) (106)
Handlebody decompositions of complex surfaces (1986) (86)
Prime knots and concordance (1979) (65)
A potential smooth counterexample in dimension 4 to the Poincare conjecture, the Schoenflies conjecture, and the Andrews-Curtis conjecture (1985) (64)
EIGHT FACES OF THE POINCARE HOMOLOGY 3-SPHERE (1979) (62)
Constructing symplectic forms on 4-manifolds which vanish on circles (2004) (45)
Constructing Lefschetz-type fibrations on four-manifolds (2007) (43)
A survey of 4-manifolds through the eyes of surgery (1998) (42)
Indefinite Morse 2-functions; broken fibrations and generalizations (2011) (39)
Normal bundles for codimension 2 locally flat imbeddings (1975) (34)
Canonical framings for 3-manifolds (1999) (34)
On the Set of Non-Locally Flat Points of a Submanifold of Codimension One (1968) (33)
HOMOLOGY 3-SPHERES BOUNDING ACYCLIC 4-MANIFOLDS (2004) (29)
Local surgery formulas for quantum invariants and the Arf invariant (2004) (28)
Akbulut's corks and h-cobordisms of smooth simply connected 4-manifolds (1997) (27)
AN EXOTIC INVOLUTION OF S4 (1979) (25)
Slice knots and property R (1978) (23)
Geometry of Low-dimensional Manifolds: Evaluations of the 3-manifold invariants of Witten and Reshetikhin-Turaev for sl (2, C) (1991) (19)
Cohomotopy sets of 4-manifolds (2012) (18)
A calculation ofPin+ bordism groups (1990) (16)
Some theorems on topological manifolds (1971) (15)
Fiber-connected, indefinite Morse 2-functions on connected n-manifolds (2011) (14)
Group trisections and smooth 4-manifolds (2016) (13)
Reconstructing 4-manifolds from Morse 2-functions (2012) (12)
A new invariant of 4-manifolds (2018) (11)
Four-Manifold Theory (1985) (11)
The union of flat $\left({n-1}\right)$-balls is flat in $R^n$ (1968) (8)
Quantum invariants at the sixth root of unity (1993) (8)
The E8–manifold, singular fibers and handlebody decompositions (1999) (5)
On the annulus conjecture (1966) (5)
Smoothing locally flat imbeddings (1966) (5)
Essay III. Some basic theorems about topological manifolds (1977) (4)
Smoothing locally flat imbeddings of differentiable manifolds (1967) (4)
Saunders Mac Lane (2005) (3)
Rohlin's theorem (1989) (1)
Wall's diffeomorphisms and H-cobordism (1989) (1)
Memories of Vaughan Jones (2021) (1)
Trisections of 4-manifolds (2018) (1)
Immersing 4-manifolds in R6 (1989) (1)
3-Manifolds; a digression (1989) (1)
Essay I. Deformation of smooth and piecewise linear manifold structures (1977) (0)
Handlebodies and framed links (1989) (0)
Local surgery (2004) (0)
MSRI Hot Topic: Floer homology for 3-manifolds. (2003) (0)
p 1 ( M ) = 3σ( M ), ω 4 so = Z and ω 4 spin = Z (1989) (0)
Exotic R4's (1989) (0)
Annex A. Stable homeomorphisms and the annulus conjecture (1977) (0)
TLie3 and \(CP^2 \mathop \sharp \limits^9 ( - CP^2 )\) (1989) (0)
Trisections and link surgeries (2019) (0)
Bounding 5-manifolds (1989) (0)
Freedman's work (1989) (0)
Low-dimensional topology and geometry (2011) (0)
Hot Topic : Floer homology for 3-manifolds . (0)
Annex B. On The Triangulation of Manifolds and the Hauptvermutung (1977) (0)

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