Locally equivalent Floer complexes and unoriented link cobordisms
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866916448094388224 |
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| author | Cavallo, Alberto |
| author_facet | Cavallo, Alberto |
| contents | We show that the local equivalence class of the collapsed link Floer complex $cCFL^\infty(L)$, together with many $Υ$-type invariants extracted from this group, is a concordance invariant of links. In particular, we define a version of the invariants $Υ_L(t)$ and $ν^+(L)$ when $L$ is a link and we prove that they give a lower bound for the slice genus $g_4(L)$. Furthermore, in the last section of the paper we study the homology group $HFL'(L)$ and its behaviour under unoriented cobordisms. We obtain that a normalized version of the $\upsilon$-set, introduced by Ozsváth, Stipsicz and Szabó, produces a lower bound for the 4-dimensional smooth crosscap number $γ_4(L)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1911_03659 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Locally equivalent Floer complexes and unoriented link cobordisms Cavallo, Alberto Geometric Topology 57K10 57K18 We show that the local equivalence class of the collapsed link Floer complex $cCFL^\infty(L)$, together with many $Υ$-type invariants extracted from this group, is a concordance invariant of links. In particular, we define a version of the invariants $Υ_L(t)$ and $ν^+(L)$ when $L$ is a link and we prove that they give a lower bound for the slice genus $g_4(L)$. Furthermore, in the last section of the paper we study the homology group $HFL'(L)$ and its behaviour under unoriented cobordisms. We obtain that a normalized version of the $\upsilon$-set, introduced by Ozsváth, Stipsicz and Szabó, produces a lower bound for the 4-dimensional smooth crosscap number $γ_4(L)$. |
| title | Locally equivalent Floer complexes and unoriented link cobordisms |
| topic | Geometric Topology 57K10 57K18 |
| url | https://arxiv.org/abs/1911.03659 |