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

Volume 27
Issue 9, 3387–3831
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
A calculus for bordered Floer homology

Jonathan Hanselman and Liam Watson

Geometry & Topology 27 (2023) 823–924
Abstract

We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form; namely, the type D structure may be described graphically by a disjoint union of loops. We develop a calculus for studying bordered invariants of this form and, in particular, provide a complete description of slopes giving rise to L–space Dehn fillings as well as necessary and sufficient conditions for L–spaces resulting from identifying two such manifolds along their boundaries. As an application, we show that Seifert-fibred spaces with torus boundary fall into this class, leading to a proof that, among graph manifolds containing a single JSJ torus, the property of being an L–space is equivalent to non-left-orderability of the fundamental group and to the nonexistence of a coorientable taut foliation.

Keywords
Heegaard Floer, bordered Floer homology, 3–manifolds, L–space conjecture
Mathematical Subject Classification 2010
Primary: 57M27
References
Publication
Received: 24 September 2015
Revised: 10 July 2020
Accepted: 20 August 2021
Published: 8 June 2023
Proposed: Peter Ozsváth
Seconded: Ciprian Manolescu, Cameron Gordon
Authors
Jonathan Hanselman
Department of Mathematics
University of Texas at Austin
Austin, TX
United States
Department of Mathematics
Princeton University
Princeton, NJ
United States
Liam Watson
School of Mathematics and Statistics
University of Glasgow
Glasgow
United Kingdom
Department of Mathematics
University of British Columbia
Vancouver BC
Canada

Open Access made possible by participating institutions via Subscribe to Open.