Stably diffeomorphic manifolds and l_{2q+1}(Z[��])

• DOI: 10.48550/arxiv.0808.2008
• Publication Date: 2008-01-01
• Authors: Crowley, Diarmuid; Sixt, J��rg
• Keywords: FOS: Mathematics; Geometric Topology (math.GT); 57R67

The monoids l_{2q+1}(Z[��]) 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[��]) \subset l_{2q+1}(Z[��]). In this paper we give exact sequences which completely describe l_{2q+1}(Z[��]) 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.<br/>v2: 46 pages: corrected the definition of [v(\bar \nu)] in section 2, altered the historical Remark 1.2, added one reference, cut inessential details and corrected some typos<br/>