Volume 19, issue 5 (2019)

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

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
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
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
Distance one lens space fillings and band surgery on the trefoil knot

Tye Lidman, Allison H Moore and Mariel Vazquez

Algebraic & Geometric Topology 19 (2019) 2439–2484
Abstract

We prove that if the lens space L(n,1) is obtained by a surgery along a knot in the lens space L(3,1) that is distance one from the meridional slope, then n is in {6,±1,±2,3,4,7}. This result yields a classification of the coherent and noncoherent band surgeries from the trefoil to T(2,n) torus knots and links. The main result is proved by studying the behavior of the Heegaard Floer d–invariants under integral surgery along knots in L(3,1). The classification of band surgeries between the trefoil and torus knots and links is motivated by local reconnection processes in nature, which are modeled as band surgeries. Of particular interest is the study of recombination on circular DNA molecules.

Keywords
lens spaces, Dehn surgery, Heegaard Floer homology, band surgery, torus knots, $d$–invariants, reconnection, DNA topology
Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R58
Secondary: 92E10
References
Publication
Received: 19 December 2017
Revised: 12 August 2018
Accepted: 16 October 2018
Published: 20 October 2019
Authors
Tye Lidman
Department of Mathematics
North Carolina State University
Raleigh, NC
United States
Allison H Moore
Department of Mathematics
University of California Davis
Davis, CA
United States
Department of Mathematics and Applied Mathematics
Virginia Commonwealth University
Richmond, VA
United States
Mariel Vazquez
Department of Mathematics, and Department of Microbiology and Molecular Genetics
University of California Davis
Davis, CA
United States