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Bordered Floer homology and existence of incompressible tori in homology spheres

  • Eaman Eftekhary (a1)
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.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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