Volume 17, issue 1 (2017)

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

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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
Three-manifold mutations detected by Heegaard Floer homology

Corrin Clarkson

Algebraic & Geometric Topology 17 (2017) 1–16

Given an orientation-preserving self-diffeomorphism φ of a closed, orientable surface S with genus at least two and an embedding f of S into a three-manifold M, we construct a mutant manifold by cutting M along f(S) and regluing by fφf1. We will consider whether there exist nontrivial gluings such that for any embedding, the manifold M and its mutant have isomorphic Heegaard Floer homology. In particular, we will demonstrate that if φ is not isotopic to the identity map, then there exists an embedding of S into a three-manifold M such that the rank of the nontorsion summands of HF̂ of M differs from that of its mutant. We will also show that if the gluing map is isotopic to neither the identity nor the genus-two hyperelliptic involution, then there exists an embedding of S into a three-manifold M such that the total rank of HF̂ of M differs from that of its mutant.

Heegaard Floer homology, mapping class group, Thurston norm, Fukaya category, three-manifolds, mutation
Mathematical Subject Classification 2010
Primary: 57M27, 57M60
Received: 16 October 2013
Revised: 8 June 2016
Accepted: 4 July 2016
Published: 26 January 2017
Corrin Clarkson
Department of Mathematics
Indiana University
831 E Third St
Bloomington, IN 47405
United States