K-theoretic invariants for Floer homology

被引:18
|
作者
Sullivan, MG [1 ]
机构
[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
基金
美国国家科学基金会;
关键词
D O I
10.1007/s00039-002-8267-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper defines two K-theoretic invariants, Wh1 and Wh(2), for individual and one-parameter families of Floor chain complexes. The chain complexes are generated by intersection points of two Lagrangian submanifolds of a symplectic manifold, and the boundary maps are determined by holomorphic curves connecting pains of intersection points. The paper proves that Wh(1) and Wh(2) do not depend on the choice of almost complex structures and are invariant under Harniltonian deformations. The proof of this invariance uses properties of holomorphic curves, parametric gluing theorems, and a stabilization process.
引用
收藏
页码:810 / 872
页数:63
相关论文
共 50 条
  • [1] K-theoretic invariants for Floer homology
    M.G. Sullivan
    [J]. Geometric & Functional Analysis GAFA, 2002, 12 : 810 - 872
  • [2] K-theoretic invariants of Hamiltonian fibrations
    Savelyev, Yasha
    Shelukhin, Egor
    [J]. JOURNAL OF SYMPLECTIC GEOMETRY, 2020, 18 (01) : 251 - 289
  • [3] Twisted K-theoretic Gromov–Witten invariants
    Valentin Tonita
    [J]. Mathematische Annalen, 2018, 372 : 489 - 526
  • [4] K-theoretic Donaldson Invariants Via Instanton Counting
    Gottsche, Lothar
    Nakajima, Hiraku
    Yoshioka, Kota
    [J]. PURE AND APPLIED MATHEMATICS QUARTERLY, 2009, 5 (03) : 1029 - 1111
  • [5] K-Theoretic Generalized Donaldson-Thomas Invariants
    Kiem, Young-Hoon
    Savvas, Michail
    [J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (03) : 2123 - 2158
  • [6] THE RANGES OF K-THEORETIC INVARIANTS FOR NONSIMPLE GRAPH ALGEBRAS
    Eilers, Soren
    Katsura, Takeshi
    Tomforde, Mark
    West, James
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 368 (06) : 3811 - 3847
  • [7] Congruences on K-theoretic Gromov-Witten invariants
    Guere, Jeremy
    [J]. GEOMETRY & TOPOLOGY, 2023, 27 (09) : 3585 - 3618
  • [8] Floer homology and invariants of homology cobordism
    Saveliev, N
    [J]. INTERNATIONAL JOURNAL OF MATHEMATICS, 1998, 9 (07) : 885 - 919
  • [9] Verlinde formulae on complex surfaces: K-theoretic invariants
    Gottsche, L.
    Kool, M.
    Williams, R. A.
    [J]. FORUM OF MATHEMATICS SIGMA, 2021, 9
  • [10] Twisted K-theoretic Gromov-Witten invariants
    Tonita, Valentin
    [J]. MATHEMATISCHE ANNALEN, 2018, 372 (1-2) : 489 - 526