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A
calculus for bordered Floer homology
Jonathan Hanselman and Liam Watson |
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Geometry & Topology 27 (2023) 823–924
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Abstract |
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We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form; namely, the type 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 –space Dehn fillings as well as necessary and sufficient conditions for –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 –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
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Mathematical Subject Classification 2010
Primary: 57M27
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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
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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 |
| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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