Stably diffeomorphic manifolds and l_{2q+1}(Z[\pi])
Geometric Topology
2008-10-23 v2
Abstract
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.
Cite
@article{arxiv.0808.2008,
title = {Stably diffeomorphic manifolds and l_{2q+1}(Z[\pi])},
author = {Diarmuid Crowley and Jörg Sixt},
journal= {arXiv preprint arXiv:0808.2008},
year = {2008}
}
Comments
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