Volume 19, issue 3 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
On uniqueness of end sums and $1$–handles at infinity

Jack S Calcut and Robert E Gompf

Algebraic & Geometric Topology 19 (2019) 1299–1339

For oriented manifolds of dimension at least 4 that are simply connected at infinity, it is known that end summing is a uniquely defined operation. Calcut and Haggerty showed that more complicated fundamental group behavior at infinity can lead to nonuniqueness. We examine how and when uniqueness fails. Examples are given, in the categories top, pl and diff, of nonuniqueness that cannot be detected in a weaker category (including the homotopy category). In contrast, uniqueness is proved for Mittag-Leffler ends, and generalized to allow slides and cancellation of (possibly infinite) collections of 0– and 1–handles at infinity. Various applications are presented, including an analysis of how the monoid of smooth manifolds homeomorphic to 4 acts on the smoothings of any noncompact 4–manifold.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

end sum, connected sum at infinity, Mittag-Leffler, semistable end, exotic smoothing
Mathematical Subject Classification 2010
Primary: 57N99, 57Q99, 57R99
Received: 8 January 2018
Revised: 3 October 2018
Accepted: 2 December 2018
Published: 21 May 2019
Jack S Calcut
Department of Mathematics
Oberlin College
Oberlin, OH
United States
Robert E Gompf
Department of Mathematics
The University of Texas at Austin
Austin, TX
United States