Kenji Fukaya
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Japanese mathematician
Kenji Fukaya's AcademicInfluence.com Rankings
Kenji Fukayamathematics Degrees
Mathematics
#372
World Rank
#765
Historical Rank
Differential Topology
#10
World Rank
#10
Historical Rank
Geometry
#14
World Rank
#30
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Measure Theory
#2880
World Rank
#3425
Historical Rank
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Mathematics
Kenji Fukaya's Degrees
- PhD Mathematics Kyoto University
Why Is Kenji Fukaya Influential?
(Suggest an Edit or Addition)According to Wikipedia, Kenji Fukaya is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry. His many fundamental contributions to mathematics include the discovery of the Fukaya category. He is a permanent faculty member at the Simons Center for Geometry and Physics and a professor of mathematics at Stony Brook University.
Kenji Fukaya'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
- ARNOLD CONJECTURE AND GROMOV–WITTEN INVARIANT (1999) (539)
- Lagrangian Intersection Floer Theory: Anomaly and Obstruction, Part I (2010) (394)
- Lagrangian Floer theory on compact toric manifolds II: bulk deformations (2008) (262)
- Collapsing of Riemannian manifolds and eigenvalues of Laplace operator (1987) (229)
- Nilpotent structures and invariant metrics on collapsed manifolds (1992) (219)
- Zero-loop open strings in the cotangent bundle and Morse homotopy (1997) (207)
- The fundamental groups of almost nonnegatively curved manifolds (1992) (179)
- A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters (1988) (141)
- Hausdorff Convergence of Riemannian Manifolds and Its Applications (1990) (139)
- Cyclic symmetry and adic convergence in Lagrangian Floer theory (2009) (138)
- Deformation theory, homological algebra and mirror symmetry (2001) (135)
- Collapsing Riemannian manifolds to ones of lower dimensions (1987) (123)
- Mirror symmetry of abelian varieties and multi-theta functions (2002) (122)
- Exact Lagrangian submanifolds in simply-connected cotangent bundles (2007) (110)
- Floer Homology and Mirror Symmetry II (2002) (89)
- The Symplectic Geometry of Cotangent Bundles from a Categorical Viewpoint (2007) (77)
- Floer homology of connected sum of homology 3-spheres (1996) (71)
- Theory of convergence for Riemannian orbifolds (1986) (71)
- Toric Degeneration and Nondisplaceable Lagrangian Tori in S2×S2 (2012) (71)
- Lagrangian Intersection Floer Theory (2009) (69)
- Collapsing Riemannian manifolds to ones with lower dimension II (1989) (69)
- Arnold conjecture and Gromov-Witten invariants for general symplectic manifolds (1999) (68)
- APPLICATION OF FLOER HOMOLOGY OF LANGRANGIAN SUBMANIFOLDS TO SYMPLECTIC TOPOLOGY (2006) (64)
- Oxidized Galectin‐1 Stimulates the Migration of Schwann Cells from Both Proximal and Distal Stumps of Transected Nerves and Promotes Axonal Regeneration after Peripheral Nerve Injury (2003) (61)
- Isometry groups of singular spaces (1994) (61)
- Lagrangian floer theory and mirror symmetry on compact toric manifolds (2010) (61)
- Counting pseudo-holomorphic discs in Calabi-Yau 3-holds (2009) (57)
- FLOER HOMOLOGY AND MIRROR SYMMETRY (1999) (52)
- Sintering of lanthanum chromite doped with zinc or copper (1988) (48)
- Lagrangian Intersection Floer Theory, Part 2: Anomaly and Obstruction, Part II (2010) (48)
- Antisymplectic involution and Floer cohomology (2009) (47)
- Technical details on Kuranishi structure and virtual fundamental chain (2012) (46)
- Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory (2011) (44)
- Homological algebra related to surfaces with boundary (2015) (35)
- Canonical models of filtered _{∞}-algebras and Morse complexes (2009) (34)
- Anti-self-dual Equation on 4-manifolds with Degenerate Metric (1998) (31)
- Lagrangian Floer theory on compact toric manifolds: survey (2010) (31)
- Morse homotopy and Chern-Simons perturbation theory (1996) (29)
- Kuranishi structure, Pseudo-holomorphic curve, and Virtual fundamental chain: Part 1 (2015) (26)
- Geometry of Gauge Fields (1996) (25)
- Anchored Lagrangian submanifolds and their Floer theory (2009) (24)
- Unobstructed immersed Lagrangian correspondence and filtered A infinity functor (2017) (23)
- Floer Homology and Gromov-Witten Invariant over Integer of General Symplectic Manifolds – Summary – (2001) (23)
- Lagrangian Floer theory over integers: spherically positive symplectic manifolds (2011) (22)
- Topology, Geometry and Field Theory (1994) (22)
- Atiyah-Floer conjecture: A formulation, a strategy of proof and generalizations (2017) (20)
- Displacement of polydisks and Lagrangian Floer theory (2011) (19)
- Kuranishi Structures and Virtual Fundamental Chains (2020) (17)
- Exponential decay estimates and smoothness of the moduli space of pseudoholomorphic curves (2016) (17)
- Toric degeneration and non-displaceable Lagrangian tori in $S^2 \times S^2$ (2010) (15)
- Gromov-Witten theory via Kuranishi structures (2017) (15)
- Floer Homology for Oriented 3-Manifolds (1992) (15)
- Shrinking good coordinate systems associated to Kuranishi structures (2014) (14)
- A finiteness theorem for negatively curved manifolds (1984) (14)
- Almost nonpositively curved manifolds (1991) (14)
- On a compactification of the set of Riemannian manifolds with bounded curvatures and diameters (1986) (12)
- Galois symmetry on Floer cohomology (2003) (11)
- Floer homology of Lagrangian submanifolds (2011) (11)
- Chapter 4 Metric Riemannian geometry (2006) (11)
- Virtual Fundamental Cycles in Symplectic Topology (2019) (10)
- $SO(3)$-Floer homology of 3-manifolds with boundary 1 (2015) (9)
- Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks: I (2017) (9)
- Differentiable Operads, the Kuranishi Correspondence, and Foundations of Topological Field Theories Based on Pseudo-Holomorphic Curves (2010) (8)
- MORSE HOMOTOPY AND ITS QUANTIZATION (1999) (7)
- Floer homology in symplectic geometry and in mirror symmetry (2006) (7)
- Expression of E-cadherin-catenin complex in human benign schwannomas. (2002) (7)
- Differentiable operad, Kuranishi correspondence, and Foundation of topological field theories (2007) (6)
- A COMPACTNESS THEOREM OF A SET OF ASPHERICAL RIEMANNIAN ORBIFOLDS (1988) (6)
- A COMPACTNESS THEOREM OF A SET OF ASPHERICAL RIEMANNIAN ORBIFOLDS (1988) (6)
- Phase Transition and Thermal Expansion of LaCrO3 Solid Solutions (1993) (5)
- Categorification of invariants in gauge theory and symplectic geometry (2017) (5)
- Lie Groupoids, Deformation of Unstable Curves, and Construction of Equivariant Kuranishi Charts (2017) (5)
- Canonical models of filtered $A_\infty$-algebras and Morse complexes (2008) (5)
- Li-Doped LaCrO3 Ceramics (1992) (4)
- Monotone Lagrangian Floer theory in smooth divisor complements: I (2018) (3)
- Loop space and holomorphic disc -summary- (2007) (3)
- Lagrangians, SO(3)-instantons and the Atiyah-Floer Conjecture (2021) (2)
- [Oblique Lumbar Interbody Fusion Combined with Minimally Invasive Percutaneous Posterior Instrumentation for Adult Spinal Deformity]. (2018) (2)
- [Risk Factors for Predicting the Need for Additional Surgery for Symptomatic Adjacent Segment Disease after Minimally Invasive Surgery-Transforaminal Lumbar Interbody Fusion]. (2017) (2)
- The Symplectic S-Cobordism Conjecture: a Summary (2021) (2)
- Reactions of Bifunctional Perfluoroarylsilanes with Activated C–F Bonds in Perfluorinated Arenes (2019) (2)
- Lagrangians, SO(3)-instantons and mixed equation (2021) (2)
- Informal note on topology, geometry and topological field theory (1997) (2)
- Floer Homology, A ∞-categories and Topological Field Theory (2021) (1)
- Floer homology, A(infinity)-categories and topological field theory (1995) (1)
- Nonpositively curved manifolds with small volume (1993) (1)
- Gromov-Hausdorff distance between filtered $A_{\infty}$ categories 1: Lagrangian Floer theory (2021) (1)
- The number of orientable small covers over a product of simplices (2018) (1)
- Construction of a linear K-system in Hamiltonian Floer theory (2021) (1)
- Homotopy equivalence of _{∞} bimodules (2010) (0)
- Global Quotients and Orbifolds (2020) (0)
- Fiber Product of Kuranishi Structures (2020) (0)
- Composition Formula of Smooth Correspondences (2020) (0)
- Zero-and One-Dimensional Cases via Multivalued Perturbation (2020) (0)
- Thickening of a Kuranishi Structure (2020) (0)
- Note on non-discrete complex hyperbolic triangle groups of type ð n; n; 1 ; k Þ II (2017) (0)
- Admissible Kuranishi Structures (2020) (0)
- Oblique Lumbar Interbody Fusion Combined with Less Invasive Percutaneous Posterior Instrumentation for Adult Spinal Deformity (2018) (0)
- Incidence of Adjacent Segment Disease after Minimally Invasive Transforaminal Lumbar Interbody Fusion (2016) (0)
- Stokes’ Formula (2020) (0)
- Extension of a Kuranishi Structure and Its Perturbation from Boundary to Its Neighborhood (2020) (0)
- Categorification of invariants in gauge theory and symplectic geometry (2017) (0)
- Tree-Like K-Systems: A ∞ Structure I – Statement (2020) (0)
- Linear K-Systems: Floer Cohomology II – Proof (2020) (0)
- Covering Space of Effective Orbifolds and K-Spaces (2020) (0)
- Foreword [Special issue: Proceedings of the VII Workshop on Symplectic and Contact Topology]. (2008) (0)
- Orbifolds and Orbibundles by Local Coordinates (2020) (0)
- Composition of KG-and GG-Embeddings: Proof of Lemma 3.34 (2020) (0)
- Construction of a linear K-system in Hamiltonian Floer theory (2022) (0)
- Weak (cid:2) -inequalities for the Haar system and differentially subordinated martingales (2012) (0)
- Linear K-Systems: Floer Cohomology III – Morse Case by Multisection (2020) (0)
- Homotopy equivalence of _{∞} algebras (2010) (0)
- Introduction to Part II (2020) (0)
- Symplectic S-cobodism Conjecture -summary (0)
- NILPOTENT STRUCTURES AND INVARIANT METRICS (2009) (0)
- On the equivalence of several definitions of compact infra-solvmanifolds (2013) (0)
- Air-fuel ratio sensor with rubber sealing bush (1997) (0)
- Local System and Smooth Correspondence in de Rham Theory with Twisted Coefficients (2020) (0)
- Classification of visible actions on flag varieties (2012) (0)
- Introduction (2020) (0)
- Bulk deformations, tropicalization and non-displaceable Lagrangian tori (2016) (0)
- A note on the Peterson hit problem for the Steenrod algebra (2021) (0)
- Stratified Submersion to a Manifold with Corners (2020) (0)
- CF-Perturbations and Integration Along the Fiber (Pushout) (2020) (0)
- Multivalued Perturbations (2020) (0)
- Kuranishi Structures and Good Coordinate Systems (2020) (0)
- Review: Floer cohomology (2010) (0)
- Notations and Conventions (2020) (0)
- Construction of Good Coordinate Systems (2020) (0)
- Linear K-Systems: Floer Cohomology I – Statement (2020) (0)
- Corner Smoothing and Composition of Morphisms (2020) (0)
- Trends in Modern Geometry (2015) (0)
- The _{∞} algebra associated to a Lagrangian submanifold (2010) (0)
- Takayasu cofibrations revisited (2015) (0)
- Construction of CF-Perturbations (2020) (0)
- From Good Coordinate Systems to Kuranishi Structures and Back with CF-Perturbations (2020) (0)
- Tree-Like K-Systems: A ∞ Structure II – Proof (2020) (0)
- Construction of Multivalued Perturbations (2020) (0)
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