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 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 $R(G)/RO(G)$.