Heegaard Floer homology and integer surgeries on links

Fuente: arXiv
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Main Authors: Manolescu, Ciprian, Ozsvath, Peter
Format: Preprint
Published: 2010
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_version_ 1866915525947293696
author Manolescu, Ciprian
Ozsvath, Peter
author_facet Manolescu, Ciprian
Ozsvath, Peter
contents Let L be a link in an integral homology three-sphere. We give a description of the Heegaard Floer homology of integral surgeries on L in terms of some data associated to L, which we call a complete system of hyperboxes for L. Roughly, a complete systems of hyperboxes consists of chain complexes for (some versions of) the link Floer homology of L and all its sublinks, together with several chain maps between these complexes. Further, we introduce a way of presenting closed four-manifolds with b_2^+ > 1 by four-colored framed links in the three-sphere. Given a link presentation of this kind for a four-manifold X, we then describe the Ozsvath-Szabo mixed invariants of X in terms of a complete system of hyperboxes for the link. Finally, we explain how a grid diagram produces a particular complete system of hyperboxes for the corresponding link.
format Preprint
id arxiv_https___arxiv_org_abs_1011_1317
institution arXiv
publishDate 2010
record_format arxiv
spellingShingle Heegaard Floer homology and integer surgeries on links
Manolescu, Ciprian
Ozsvath, Peter
Geometric Topology
57R58, 57R57
Let L be a link in an integral homology three-sphere. We give a description of the Heegaard Floer homology of integral surgeries on L in terms of some data associated to L, which we call a complete system of hyperboxes for L. Roughly, a complete systems of hyperboxes consists of chain complexes for (some versions of) the link Floer homology of L and all its sublinks, together with several chain maps between these complexes. Further, we introduce a way of presenting closed four-manifolds with b_2^+ > 1 by four-colored framed links in the three-sphere. Given a link presentation of this kind for a four-manifold X, we then describe the Ozsvath-Szabo mixed invariants of X in terms of a complete system of hyperboxes for the link. Finally, we explain how a grid diagram produces a particular complete system of hyperboxes for the corresponding link.
title Heegaard Floer homology and integer surgeries on links
topic Geometric Topology
57R58, 57R57
url https://arxiv.org/abs/1011.1317