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- W4367191102 abstract "This paper gives a geometric interpretation of bordered Heegaard Floer homology for manifolds with torus boundary. If $M$ is such a manifold, we show that the type D structure $widehat{mathit{CFD}}$ may be viewed as a set of immersed curves decorated with local systems in $partial M$. These curves-with-decoration are invariants of the underlying three-manifold up to regular homotopy of the curves and isomorphism of the local systems. Given two such manifolds and a homeomorphism $h$ between the boundary tori, the Heegaard Floer homology of the closed manifold obtained by gluing with $h$ is obtained from the Lagrangian intersection Floer homology of the curve-sets. This machinery has several applications: We establish that the dimension of $widehat{mathit{HF}}$ decreases under a certain class of degree one maps (pinches) and we establish that the existence of an essential separating torus gives rise to a lower bound on the dimension of $widehat{mathit{HF}}$. In particular, it follows that a prime rational homology sphere $Y$ with $widehat{mathit{HF}}(Y)<5$ must be geometric. Other results include a new proof of Eftekhary's theorem that L-space homology spheres are atoroidal; a complete characterisation of toroidal L-spaces in terms of gluing data; and a proof of a conjecture of Hom, Lidman, and Vafaee on satellite L-space knots." @default.
- W4367191102 created "2023-04-28" @default.
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- W4367191102 date "2016-04-12" @default.
- W4367191102 modified "2023-10-17" @default.
- W4367191102 title "Bordered Floer homology for manifolds with torus boundary via immersed curves" @default.
- W4367191102 doi "https://doi.org/10.48550/arxiv.1604.03466" @default.
- W4367191102 hasPublicationYear "2016" @default.
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