Journal of the Mathematical Society of Japan

Equivariant version of Rochlin-type congruences

Mikio FURUTA and Yukio KAMETANI

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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 Spin$^c$-$G$-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 Spin$^c$-$G$-manifolds with spin boundary, where we define equivariant indices with values in $R(G)/RO(G)$.

Article information

Source
J. Math. Soc. Japan, Volume 66, Number 1 (2014), 205-221.

Dates
First available in Project Euclid: 24 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1390600842

Digital Object Identifier
doi:10.2969/jmsj/06610205

Mathematical Reviews number (MathSciNet)
MR3161398

Zentralblatt MATH identifier
1326.19004

Subjects
Primary: 19K56: Index theory [See also 58J20, 58J22]
Secondary: 57S15: Compact Lie groups of differentiable transformations

Keywords
equivariant index spin structure

Citation

FURUTA, Mikio; KAMETANI, Yukio. Equivariant version of Rochlin-type congruences. J. Math. Soc. Japan 66 (2014), no. 1, 205--221. doi:10.2969/jmsj/06610205. https://projecteuclid.org/euclid.jmsj/1390600842


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