Stably diffeomorphic manifolds and l_2q+1(Z[π])

2008/08/14 by Diarmuid Crowley, Crowley, Diarmuid, Joerg Sixt +2
Mathematics · #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57R67

paper · pdf · doi:10.48550/arxiv.0808.2008

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

arxiv created 2008/10/23 · arxiv updated 2009/12/01

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]) ⊂ 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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