Equivariant version of Rochlin-type congruences. (English) Zbl 1326.19004
Summary: W. Zhang [C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 305–308 (1992; Zbl 0767.57015); C. R. Acad. Sci., Paris, Sér. I 317, No. 7, 689–692 (1993; Zbl 0804.57012)] 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 \(\mathrm{Spin}^c-G\)-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 \(\mathrm{Spin}^c-G\)-manifolds with spin boundary, where we define equivariant indices with values in \(R(G)/RO(G)\).
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