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

Diarmuid Crowley; Jörg Sixt

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arXiv · 0808.2008

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

Diarmuid Crowley·Jörg Sixt

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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.

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BibTeX RIS

Diarmuid Crowley, Jörg Sixt. 2008-10-23. Stably diffeomorphic manifolds and l_{2q+1}(Z[π]). https://arxiv.org/abs/0808.2008

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