Cobordism groups of simple branched coverings

Abstract

Abstract. We consider branched coverings which are simple in the sense that any point of the target has at most one singular preimage. The cobordism classes of k-fold simple branched coverings between n-manifolds form an abelian group Cob 1 (n, k). Moreover, Cob 1 ( * , k) = ∞ n=0 Cob 1 (n, k) is a module over Ω SO * . We construct a universal k-fold simple branched covering, and use it to compute this module rationally. As a corollary, we determine the rank of the groups Cob 1 (n, k). In the case n = 2 we compute the group Cob 1 (2, k), give a complete set of invariants and construct generators.