Volume 21, issue 5 (2021)

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

Volume 22
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Surgeries, sharp $4$–manifolds and the Alexander polynomial

Duncan McCoy

Algebraic & Geometric Topology 21 (2021) 2649–2676
Abstract

Work of Ni and Zhang has shown that, for the torus knot Tr,s with r > s > 1, every surgery slope pq 30 67(r2 1)(s2 1) is a characterizing slope. We show that this can be lowered to a bound which is linear in rs, namely pq 43 4 (rs r s). The main technical ingredient in this improvement is to show that if Y is an L–space bounding a sharp 4–manifold which is obtained by pq–surgery on a knot K in S3 and pq exceeds 4g(K) + 4, then the Alexander polynomial of K is uniquely determined by Y and pq. We also show that if pq–surgery on K bounds a sharp 4–manifold, then Spq3(K) bounds a sharp 4–manifold for all pq pq.

Keywords
Dehn surgery, sharp 4–manifolds, characterizing slopes, changemaker lattices
Mathematical Subject Classification
Primary: 57K10, 57K18
References
Publication
Received: 2 August 2020
Revised: 2 October 2020
Accepted: 20 October 2020
Published: 31 October 2021
Authors
Duncan McCoy
Département de mathématiques
Université du Québec à Montréal
Montreal, QC
Canada