Spherical alterations of handles: embedding the manifold plus construction

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

2011-08-25

arxiv.org/abs/1108.5166v1

Mathematics

Geometric Topology

22 pages, 4 figures

Scientific paper

A key tool in our earlier work on ends of manifolds high-dimensional manifolds was an ability to embed cobordisms provided by the Quillen Plus Construction into those ends. Here we develop a `spherical modification' trick which provides a constructive approach to obtaining such embeddings. More importantly, this approach allows for more general embedding results. In this paper we develop generalizations of the plus construction and show how the corresponding cobordisms can be embedded in manifolds satisfying appropriate fundamental group properties. Results obtained here play an important role in our ongoing study of noncompact manifolds.

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