Bordered Floer homology and incompressible surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866915974508183552 |
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| author | Alishahi, Akram Lipshitz, Robert |
| author_facet | Alishahi, Akram Lipshitz, Robert |
| contents | We show that bordered Heegaard Floer homology detects incompressible surfaces and bordered-sutured Floer homology detects partly boundary parallel tangles and bridges, in natural ways. For example, there is a bimodule Lambda so that the tensor product of CFD(Y) and Lambda is Hom-orthogonal to CFD(Y) if and only if the boundary of Y admits an essential compressing disk. In the process, we sharpen a nonvanishing result of Ni's. We also extend Lipshitz-Ozsváth-Thurston's "factoring" algorithm for computing HF-hat to compute bordered-sutured Floer homology, to make both results on detecting incompressibility practical. In particular, this makes Zarev's tangle invariant manifestly combinatorial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1708_05121 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Bordered Floer homology and incompressible surfaces Alishahi, Akram Lipshitz, Robert Geometric Topology We show that bordered Heegaard Floer homology detects incompressible surfaces and bordered-sutured Floer homology detects partly boundary parallel tangles and bridges, in natural ways. For example, there is a bimodule Lambda so that the tensor product of CFD(Y) and Lambda is Hom-orthogonal to CFD(Y) if and only if the boundary of Y admits an essential compressing disk. In the process, we sharpen a nonvanishing result of Ni's. We also extend Lipshitz-Ozsváth-Thurston's "factoring" algorithm for computing HF-hat to compute bordered-sutured Floer homology, to make both results on detecting incompressibility practical. In particular, this makes Zarev's tangle invariant manifestly combinatorial. |
| title | Bordered Floer homology and incompressible surfaces |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/1708.05121 |