Equivariant version of Rochlin-type congruences

Mikio Furuta, Yukio Kametani

Research output: Contribution to journalArticle

Abstract

W. Zhang showed a higher dimensional version of Rochlin congruence for 8k+4-dimensional manifolds. We give an equivariant version of Zhang's theorem for 8k+4-dimensional compact Spinc-G-manifolds with spin boundary, where we define equivariant indices with values in R(G)/RSp(G). We also give a similar congruence relation for 8k-dimensional compact Spinc- G-manifolds with spin boundary, where we define equivariant indices with values in R(G)/RO(G).

Original languageEnglish
Pages (from-to)205-221
Number of pages17
JournalJournal of the Mathematical Society of Japan
Volume66
Issue number1
DOIs
Publication statusPublished - 2014

Fingerprint

Equivariant
G-manifolds
Congruence
Congruence Relation
High-dimensional
Theorem

Keywords

  • Equivariant index
  • Spin structure

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Equivariant version of Rochlin-type congruences. / Furuta, Mikio; Kametani, Yukio.

In: Journal of the Mathematical Society of Japan, Vol. 66, No. 1, 2014, p. 205-221.

Research output: Contribution to journalArticle

@article{16dfe6a23c764217be1cd9ea2f0e7363,
title = "Equivariant version of Rochlin-type congruences",
abstract = "W. Zhang showed a higher dimensional version of Rochlin congruence for 8k+4-dimensional manifolds. We give an equivariant version of Zhang's theorem for 8k+4-dimensional compact Spinc-G-manifolds with spin boundary, where we define equivariant indices with values in R(G)/RSp(G). We also give a similar congruence relation for 8k-dimensional compact Spinc- G-manifolds with spin boundary, where we define equivariant indices with values in R(G)/RO(G).",
keywords = "Equivariant index, Spin structure",
author = "Mikio Furuta and Yukio Kametani",
year = "2014",
doi = "10.2969/jmsj/06610205",
language = "English",
volume = "66",
pages = "205--221",
journal = "Journal of the Mathematical Society of Japan",
issn = "0025-5645",
publisher = "Mathematical Society of Japan - Kobe University",
number = "1",

}

TY - JOUR

T1 - Equivariant version of Rochlin-type congruences

AU - Furuta, Mikio

AU - Kametani, Yukio

PY - 2014

Y1 - 2014

N2 - W. Zhang showed a higher dimensional version of Rochlin congruence for 8k+4-dimensional manifolds. We give an equivariant version of Zhang's theorem for 8k+4-dimensional compact Spinc-G-manifolds with spin boundary, where we define equivariant indices with values in R(G)/RSp(G). We also give a similar congruence relation for 8k-dimensional compact Spinc- G-manifolds with spin boundary, where we define equivariant indices with values in R(G)/RO(G).

AB - W. Zhang showed a higher dimensional version of Rochlin congruence for 8k+4-dimensional manifolds. We give an equivariant version of Zhang's theorem for 8k+4-dimensional compact Spinc-G-manifolds with spin boundary, where we define equivariant indices with values in R(G)/RSp(G). We also give a similar congruence relation for 8k-dimensional compact Spinc- G-manifolds with spin boundary, where we define equivariant indices with values in R(G)/RO(G).

KW - Equivariant index

KW - Spin structure

UR - http://www.scopus.com/inward/record.url?scp=84894165855&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894165855&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06610205

DO - 10.2969/jmsj/06610205

M3 - Article

AN - SCOPUS:84894165855

VL - 66

SP - 205

EP - 221

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 1

ER -