LOCALIZATION OF CHERN-SIMONS TYPE INVARIANTS OF RIEMANNIAN FOLIATIONS

被引：6
作者：
Goertsches, Oliver [1 ]
Nozawa, Hiraku [2 ]
Toben, Dirk [3 ]
机构：
[1] Philipps Univ Marburg, Fachbereich Math & Informat, Hans Meerwein Str, D-35032 Marburg, Germany
[2] Ritsumeikan Univ, Dept Math Sci, Coll Sci & Engn, 1-1-1 Nojihigashi, Shiga 5258577, Japan
[3] Univ Fed Sao Carlos, Dept Matemat, Rod Washington Luis,Km 235 CP 676, BR-13565905 Sao Carlos, SP, Brazil
来源：
ISRAEL JOURNAL OF MATHEMATICS | 2017年 / 222卷 / 02期
关键词：
SASAKI-EINSTEIN MANIFOLDS; WEIL MEASURES; CO-HOMOLOGY; DUALITY; FORMS; COHOMOLOGY; FINITENESS; TENSENESS; GEOMETRY; THEOREM;
D O I：
10.1007/s11856-017-1608-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove an Atiyah-Bott-Berline-Vergne type localization formula for Killing foliations in the context of equivariant basic cohomology. As an application, we localize some Chern-Simons type invariants, for example the volume of Sasakian manifolds and secondary characteristic classes of Riemannian foliations, to the union of closed leaves. Various examples are given to illustrate our method.
引用
收藏
页码：867 / 920
页数：54
相关论文
共 57 条
  • [1] [Anonymous], 2008, OXFORD MATH MONOGRAP
  • [2] [Anonymous], 1972, J. Differential Geometry
  • [3] [Anonymous], 2001, J. Symplectic Geom.
  • [4] [Anonymous], 1997, MONOGRAPHS MATH
  • [5] [Anonymous], 1983, REPRESENTATION THEOR
  • [6] [Anonymous], 1972, Pure and Applied Mathematics
  • [7] Asuke, 2010, MSJ MEMOIRS, V24
  • [8] Localization and residue of the Bott class
    Asuke, T
    [J]. TOPOLOGY, 2004, 43 (02) : 289 - 317
  • [9] THE MOMENT MAP AND EQUIVARIANT CO-HOMOLOGY
    ATIYAH, MF
    BOTT, R
    [J]. TOPOLOGY, 1984, 23 (01) : 1 - 28
  • [10] On characteristics of circle-invariant presymplectic forms
    Banyaga, A
    Rukimbira, P
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (12) : 3901 - 3906
123456