Algebraic & Geometric Topology

Spherical alterations of handles: embedding the manifold plus construction

Craig R Guilbault and Frederick C Tinsley

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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.

Article information

Algebr. Geom. Topol., Volume 13, Number 1 (2013), 35-60.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57N15: Topology of $E^n$ , $n$-manifolds ($4 \less n \less \infty$) 57Q12: Wall finiteness obstruction for CW-complexes
Secondary: 57Q10: Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28] 57R65: Surgery and handlebodies

spherical alteration perfect group plus construction generalized plus construction


Guilbault, Craig R; Tinsley, Frederick C. Spherical alterations of handles: embedding the manifold plus construction. Algebr. Geom. Topol. 13 (2013), no. 1, 35--60. doi:10.2140/agt.2013.13.35.

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