Stably diffeomorphic manifolds and l_{2q+1}(Z[π])
arXiv:0808.2008
Abstract
The monoids l_{2q+1}(Z[π]) detect s-cobordisms amongst certain bordisms between stably diffeomorphic 2q-dimensional manifolds and generalise the Wall simple surgery obstruction groups, L_{2q+1}^s(Z[π]) \subset l_{2q+1}(Z[π]). In this paper we give exact sequences which completely describe l_{2q+1}(Z[π]) as a set and which we use to compute its Grothendieck group. As a consequence we deduce cancellation results for stably diffeomorphic manifolds with polycyclic-by-finite fundamental group.
v2: 46 pages: corrected the definition of [v(\bar ν)] in section 2, altered the historical Remark 1.2, added one reference, cut inessential details and corrected some typos