Peter B. Kronheimer

Peter B. Kronheimer's AcademicInfluence.com Rankings

Peter B. Kronheimer

Mathematics

#1776

World Rank

#2842

Historical Rank

Measure Theory

#3157

World Rank

#3742

Historical Rank

mathematics Degrees

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Mathematics

Why Is Peter B. Kronheimer Influential?

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According to Wikipedia, Peter Benedict Kronheimer is a British mathematician, known for his work on gauge theory and its applications to 3- and 4-dimensional topology. He is William Caspar Graustein Professor of Mathematics at Harvard University and former chair of the mathematics department.

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Peter B. Kronheimer'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

The construction of ALE spaces as hyper-Kähler quotients (1989) (649)
The Genus of Embedded Surfaces in the Projective Plane (1994) (521)
Monopoles and Three-Manifolds (2008) (399)
Yang-Mills instantons on ALE gravitational instantons (1990) (314)
Khovanov homology is an unknot-detector (2010) (271)
Gauge theory for embedded surfaces, II (1993) (267)
Monopoles and lens space surgeries (2003) (260)
A Torelli-type theorem for gravitational instantons (1989) (235)
Embedded surfaces and the structure of Donaldson's polynomial invariants (1995) (198)
Monopoles and contact structures (1997) (181)
Instantons and the geometry of the nilpotent variety (1990) (161)
Knots, sutures, and excision (2008) (153)
Gauge theory for embedded surfaces , II (1997) (144)
Witten's conjecture and Property P (2003) (137)
A Hyper‐KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group (1990) (135)
Knot homology groups from instantons (2008) (131)
Recurrence relations and asymptotics for four-manifold invariants (1994) (90)
FLOER HOMOLOGY GROUPS IN YANG–MILLS THEORY (Cambridge Tracts in Mathematics 147) By S. K. D ONALDSON : 236 pp., £50.00 (US$75.00), ISBN 0 521 80803 0 (Cambridge University Press, 2002). (2003) (76)
Minimal genus in S1×M3 (1999) (74)
Dehn surgery, the fundamental group and SU(2) (2003) (73)
GAUGE THEORY FOR EMBEDDED SURFACES, I (2001) (68)
Embedded Surfaces and Guage Theory in Three and Four Dimensions (1996) (68)
Scalar curvature and the Thurston norm (1997) (57)
A hyperkahler structure on the cotangent bundle of a complex Lie group (2004) (56)
Instanton Floer homology and the Alexander polynomial (2009) (53)
Four-manifold invariants from higher-rank bundles (2004) (47)
Minimal genus in S 1 × M 3 (1997) (46)
Gauge theory and Rasmussen's invariant (2011) (44)
Some non-trivial families of symplectic structures (1997) (37)
Tait colorings, and an instanton homology for webs and foams (2015) (34)
PERIODIC FLOER PRO-SPECTRA FROM THE SEIBERG-WITTEN EQUATIONS (2002) (30)
An obstruction to removing intersection points in immersed surfaces (1997) (27)
Dehn surgery, the fundamental group and {\itshape SU}(2) (2004) (26)
Filtrations on instanton homology (2011) (20)
Instanton invariants and flat connections on the Kummer surface (1991) (20)
{\boldmath{$\operatorname{PU}(2)$} monopoles and a conjecture of Mariño, Moore, and Peradze (1998) (17)
A deformation of instanton homology for webs (2017) (17)
The genus-minimizing property of algebraic curves (1993) (15)
The structure of Donaldson ’ s invariants for four-manifolds not of simple type (1997) (15)
Exact triangles for SO(3) instanton homology of webs (2015) (15)
The Dehn twist on a sum of two $K3$ surfaces (2020) (15)
The Tripos Problem (1981) (14)
Instantons and some concordance invariants of knots (2019) (14)
Bézout’s theorem (2007) (11)
SCALAR CURVATURE AND THE THURSTON (2004) (8)
Instantons and Bar-Natan homology (2019) (6)
Casson's invariant and quadratic reciprocity (1991) (6)
Dehn twist on a sum of two K 3 surfaces (2020) (3)
Mutation and instanton knot homology (2010) (2)
Kakutani’s theorem for real-valued maps on a compact surface (1982) (1)
Instantons, Bar-Natan homology, and some concordance invariants of knots. (2019) (1)
Memories of Sir Michael Atiyah (2019) (1)
Developments in Symplectic Topology (1998) (1)
Corrigendum to : Gauge theory and Rasmussen ’ s invariant (2019) (1)
Level triangles on a surface with boundary (1985) (1)
KNOTS, THREE-MANIFOLDS AND INSTANTONS (2019) (1)
The n -Dimensional Simple Tripos Problem (1985) (0)
Monopoles and Three-Manifolds: References (2007) (0)
Monopoles and Three-Manifolds: Moduli spaces and transversality (2007) (0)
Slice Knots and the Concordance Group (2009) (0)
New Developments in the Theory of Knots; The Geometry and Physics of Knots; The Geometry of Four‐Manifolds (1992) (0)
MSRI Hot Topic: Floer homology for 3-manifolds. (2003) (0)
Monopoles and Three-Manifolds: Floer homology (2007) (0)
Monopoles and Three-Manifolds: Non-exact perturbations (2007) (0)
ec 2 00 3 Witten ’ s conjecture and Property P (0)
Relations in singular instanton homology (2022) (0)
THE GENUS-MINIMIZING PROPERTY OF ALGEBRAIC CURVES P. B. Kronheimer (1993) (0)
Monopoles and Three-Manifolds: Compactness and gluing (2007) (0)
The Seiberg–Witten equations and compactness (2007) (0)
Cobordisms and invariance (2007) (0)
Hilbert manifolds and perturbations (2007) (0)
AND CIPRIAN MANOLESCU in the sense (2014) (0)
Monopoles and Three-Manifolds: Further developments (2007) (0)
Random Fourier series and Brownian motion (2010) (0)
3 0 N ov 2 00 3 Witten ’ s conjecture and Property (2008) (0)

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