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On the set of L-space surgeries for links

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HTL - Homology theories in low dimensional topology

A 3 -manifold is called an L-space if its Heegaard Floer homology has minimal possible rank. A link (or knot) is called an L-space link if all sufficiently large surgeries of the three-sphere along its components are L-spaces. It is well known that the set of L-space surgeries for a nontrivial L-space knot is a half-line. Quite surprisingly, even for links with 2 components this set could have a complicated structure. I will prove that for “most” L-space links (in particular, for most algebraic links) this set is bounded from below, and show some nontrivial examples where it is unbounded. This is a joint work with Andras Nemethi.



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