TY - JOUR

T1 - A calculus for bordered Floer homology

AU - Hanselman, Jonathan

AU - Watson, Liam

N1 - Funding Information:
Hanselman was partially supported by NSF RTG grant DMS-1148490. Watson was partially supported by a Marie Curie Career Integration Grant (HFFUNDGRP).
Publisher Copyright:
© 2023 MSP.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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U2 - 10.2140/gt.2023.27.823

DO - 10.2140/gt.2023.27.823

M3 - Article

AN - SCOPUS:85163170194

SN - 1465-3060

VL - 27

SP - 823

EP - 924

JO - Geometry and Topology

JF - Geometry and Topology

IS - 3

ER -