Heegaard Floer homology and integer surgeries on links
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arXiv
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| Format: | Preprint |
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2010
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| _version_ | 1866915525947293696 |
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| 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 |