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Bordered Floer homology and existence of incompressible tori in homology spheres

Part of: Low-dimensional topology Differential topology

Published online by Cambridge University Press:  18 May 2018

Eaman Eftekhary
Eaman Eftekhary*
Affiliation:
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5746, Tehran, Iran email [email protected]
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Abstract

Let $Y$ be a homology sphere which contains an incompressible torus. We show that $Y$ cannot be an $L$-space, i.e. the rank of $\widehat{\text{HF}}(Y)$ is greater than $1$. In fact, if the homology sphere $Y$ is an irreducible $L$-space, then $Y$ is $S^{3}$, the Poincaré sphere $\unicode[STIX]{x1D6F4}(2,3,5)$ or hyperbolic.

Keywords

Floer homologysplicingincompressible torus

MSC classification

Primary: 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 6 , June 2018 , pp. 1222 - 1268
Copyright
© The Author 2018 

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