Volume 16, issue 3 (2016)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Exotic smoothings via large $\mathbb{R}^4$'s in Stein surfaces

Julia Bennett

Algebraic & Geometric Topology 16 (2016) 1637–1681
Abstract

We study the relationship between exotic 4’s and Stein surfaces as it applies to smoothing theory on more general open 4–manifolds. In particular, we construct the first known examples of large exotic 4’s that embed in Stein surfaces. This relies on an extension of Casson’s embedding theorem for locating Casson handles in closed 4–manifolds. Under sufficiently nice conditions, we show that using these 4’s as end-summands produces uncountably many diffeomorphism types while maintaining independent control over the genus-rank function and the Taylor invariant.

Keywords
exotic smooth structures, open $4$–manifolds, Stein surfaces
Mathematical Subject Classification 2010
Primary: 57N13
Secondary: 57R55
References
Publication
Received: 25 November 2014
Revised: 20 September 2015
Accepted: 29 September 2015
Published: 1 July 2016
Authors
Julia Bennett
Department of Mathematics
University of Texas at Austin
Austin, TX 78712
United States