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