## Algebraic & Geometric Topology

### Spherical alterations of handles: embedding the manifold plus construction

#### 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.

#### Article information

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

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

https://projecteuclid.org/euclid.agt/1513715491

Digital Object Identifier
doi:10.2140/agt.2013.13.35

Mathematical Reviews number (MathSciNet)
MR3031636

Zentralblatt MATH identifier
06138571

#### Citation

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. https://projecteuclid.org/euclid.agt/1513715491

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