LAUSR

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 $${{\rm Cob}^1(n, k)}$$Cob1(n,k). Moreover, $${{\rm Cob}^1(*, k) = \bigoplus_{n = 0}^{\infty}{\rm Cob}^1(n, k)}$$Cob1(∗,k)=⨁n=0∞Cob1(n,k) is a module over $${\Omega^{SO}_{*}}$$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 $${{\rm Cob}^1(n, k)}$$Cob1(n,k). In the case n =  2 we compute the group $${{\rm Cob}^1(2, k)}$$Cob1(2,k), give a complete set of invariants and construct generators.