The Godbillon-Vey invariant and equivariant K K-theory

被引：3
作者：
MacDonald, Lachlan [1 ]
Rennie, Adam [1 ]
机构：
[1] Univ Wollongong, Sch Math & Appl Stat, Wollongong, NSW, Australia
来源：
ANNALS OF K-THEORY | 2020年 / 5卷 / 02期
关键词：
foliation; Godbillon-Vey; bivariant K-theory; equivariant; spectral triple; LOCAL INDEX FORMULA; CYCLIC COHOMOLOGY; NONCOMMUTATIVE GEOMETRY; SECONDARY CLASSES; CHERN CHARACTER; HOPF-ALGEBRAS; FOLIATIONS; GROUPOIDS; OPERATORS; DYNAMICS;
D O I：
10.2140/akt.2020.5.249
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We construct a groupoid equivariant Kasparov class for transversely oriented foliations in all codimensions. In codimension 1 we show that the Chern character of an associated semifinite spectral triple recovers the Connes-Moscovici cyclic cocycle for the Godbillon-Vey secondary characteristic class.
引用
收藏
页码：249 / 294
页数：46
相关论文
共 61 条
  • [1] A Baum-Connes conjecture for singular foliations
    Androulidakis, Iakovos
    Skandalis, Georges
    [J]. ANNALS OF K-THEORY, 2019, 4 (04) : 561 - 620
  • [2] [Anonymous], Lecture Notes in Mathematics
  • [3] BAAJ S, 1983, CR ACAD SCI I-MATH, V296, P875
  • [4] Transverse noncommutative geometry of foliations
    Benameur, Moulay-Tahar
    Heitsch, James L.
    [J]. JOURNAL OF GEOMETRY AND PHYSICS, 2018, 134 : 161 - 194
  • [5] Type II non-commutative geometry. I. Dixmier trace in von Neumann algebras
    Benameur, MT
    Fack, T
    [J]. ADVANCES IN MATHEMATICS, 2006, 199 (01) : 29 - 87
  • [6] CHARACTERISTIC CLASSES OF GAMMA-FOLIATIONS
    BOTT, R
    HAEFLIGER, A
    [J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 78 (06) : 1039 - 1044
  • [7] BOTT R., 1970, Global Analysis, VXVI, P127
  • [8] Bott R., 1972, Lectures on Algebraicand Differential Topology, V279, P1
  • [9] BOTT R, 1976, ASTERISQUE, V32, P113
  • [10] Candel A., 2000, GRADUATE STUDIES MAT, V23
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