Compact Lie group action and equivariant bordism

Abstract

Let G G be a compact Lie group and H H a compact Lie subgroup of G G contained in the center of G G with H m {H^m} the maximal subgroup in the center, H H being H H -boundary. Let p r : H m → H pr:{H^m} \to H be the projection onto the r r th factor and H r {H_r} be the r r th factor of H m {H^m} . Let { L r } \{ {L_r}\} be a family of subgroups of G G such that L r ∩ H r {L_r} \cap {H_r} is nontrivial. Consider a G G -manifold M n {M^n} with p r ( G x ∩ H m ) pr({G_x} \cap {H^m}) trivial or containing L r {L_r} , for every x x in M n {M^n} . The main result of the paper is that if ∀ x ∈ M n \forall x \in {M^n} , p r ( G x ∩ H m ) {p_r}({G_x} \cap {H^m}) is trivial at least for one r r , then M n {M^n} is a G G -boundary.