# Connected sum at infinity and 4-manifolds

## 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≥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.

## Repository Citation

Calcut, Jack S. and Patrick V. Haggerty. 2014. "Connected sum at infinity and 4-manifolds." Algebraic & Geometric Topology 14: 3281-3303.

## Publisher

Mathematical Sciences Publishers

## Publication Date

1-1-2014

## Publication Title

Algebraic & Geometric Topology

## Department

Mathematics

## Document Type

Article

## DOI

https://dx.doi.org/10.2140/agt.2014.14.3281

## Keywords

Connected sum at infinity, End sum, Ladder manifold, Cohomology algebra at infinity, Proper homotopy, Direct limit, Stringer sum, Lens space

## Language

English

## Format

text