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

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

2008-08-14

arxiv.org/abs/0808.2008v2

Mathematics

Geometric Topology

v2: 46 pages: corrected the definition of [v(\bar \nu)] in section 2, altered the historical Remark 1.2, added one reference,

Scientific paper

The monoids l_{2q+1}(Z[\pi]) 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[\pi]) \subset l_{2q+1}(Z[\pi]). In this paper we give exact sequences which completely describe l_{2q+1}(Z[\pi]) 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.

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