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).