Connected sum at infinity and 4–manifolds

Calcut, Jack S; Haggerty, Patrick V

doi:10.2140/agt.2014.14.3281

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Connected sum at infinity and $4$–manifolds

Jack S Calcut and Patrick V Haggerty

Algebraic & Geometric Topology 14 (2014) 3281–3303

DOI: 10.2140/agt.2014.14.3281

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 $m \geq 3$ , 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

Mathematical Subject Classification 2010

Primary: 57R19

Secondary: 55P57

References

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

Volume 14, issue 6 (2014)