#### Volume 14, issue 6 (2014)

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Connected sum at infinity and $4$–manifolds

### Jack S Calcut and Patrick V Haggerty

Algebraic & Geometric Topology 14 (2014) 3281–3303
##### Abstract

We study connected sum at infinity on smooth, open manifolds. This operation requires a choice of proper ray in each manifold summand. In favorable circumstances, the connected sum at infinity operation is independent of ray choices. For each $m\ge 3$, we construct an infinite family of pairs of $m$–manifolds on which the connected sum at infinity operation yields distinct manifolds for certain ray choices. We use cohomology algebras at infinity to distinguish these manifolds.

##### Keywords
connected sum at infinity, end sum, ladder manifold, cohomology algebra at infinity, proper homotopy, direct limit, stringer sum, lens space
Primary: 57R19
Secondary: 55P57
##### Publication
Received: 30 April 2013
Revised: 26 January 2014
Accepted: 7 February 2014
Published: 15 January 2015
##### Authors
 Jack S Calcut Department of Mathematics Oberlin College Oberlin, OH 44074 USA http://www.oberlin.edu/faculty/jcalcut/ Patrick V Haggerty Department of Mathematics Indiana University Bloomington, IN 47405 USA