A calculus for bordered Floer homology

Hanselman, Jonathan¹ ; Watson, Liam²

¹ Department of Mathematics, University of Texas at Austin, Austin, TX, United States, Department of Mathematics, Princeton University, Princeton, NJ, United States
² School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom, Department of Mathematics, University of British Columbia, Vancouver BC, Canada

Geometry & topology, Tome 27 (2023) no. 3, pp. 823-924.

Résumé

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.

Détail

DOI : 10.2140/gt.2023.27.823

Classification : 57M27
Keywords: Heegaard Floer, bordered Floer homology, 3–manifolds, L–space conjecture

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