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2013 Spherical alterations of handles: embedding the manifold plus construction
Craig R Guilbault, Frederick C Tinsley
Algebr. Geom. Topol. 13(1): 35-60 (2013). 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.

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Craig R Guilbault. Frederick C Tinsley. "Spherical alterations of handles: embedding the manifold plus construction." Algebr. Geom. Topol. 13 (1) 35 - 60, 2013. https://doi.org/10.2140/agt.2013.13.35

Information

Received: 11 August 2011; Revised: 10 January 2012; Accepted: 17 August 2012; Published: 2013
First available in Project Euclid: 19 December 2017

MathSciNet: MR3031636
zbMATH: 06138571
Digital Object Identifier: 10.2140/agt.2013.13.35

Subjects:
Primary: 57N15, 57Q12
Secondary: 57Q10, 57R65

Rights: Copyright © 2013 Mathematical Sciences Publishers

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