Spherical alterations of handles: embedding the manifold plus construction

Guilbault, Craig R; Tinsley, Frederick C

doi:10.2140/agt.2013.13.35

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Spherical alterations of handles: embedding the manifold plus construction

Craig R Guilbault and Frederick C Tinsley

Algebraic & Geometric Topology 13 (2013) 35–60

DOI: 10.2140/agt.2013.13.35

Abstract

Quillen’s famous plus construction plays an important role in many aspects of manifold topology. In our own work [Geometry and Topology 7 (2006) 541–556] on ends of open manifolds, an ability to embed cobordisms provided by the plus construction into the manifolds being studied was a key to completing the main structure theorem. In this paper we develop a “spherical modification” trick that allows for a constructive approach to obtaining those embeddings. More importantly, this approach can be used to obtain more general embedding results. In this paper we develop generalizations of the plus construction (together with the corresponding group-theoretic notions) and show how those cobordisms can be embedded in manifolds satisfying appropriate fundamental group properties. Results obtained here are motivated by, and play an important role in, our ongoing study of noncompact manifolds.

Keywords

spherical alteration, perfect group, plus construction, generalized plus construction

Mathematical Subject Classification 2010

Primary: 57N15, 57Q12

Secondary: 57Q10, 57R65

References

Publication

Received: 11 August 2011

Revised: 10 January 2012

Accepted: 17 August 2012

Published: 6 February 2013

Authors

Craig R Guilbault
Department of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee, WI 53201 USA
http://https://pantherfile.uwm.edu/craigg/www/
Frederick C Tinsley
Department of Mathematics & Computer Science Colorado College 14 East Cache La Poudre St Colorado Springs, CO 80903 USA
http://faculty1.coloradocollege.edu/~ftinsley/

Volume 13, issue 1 (2013)