Rigidity of the saddle connection complex
For a half-translation surface (S,q)$(S,q)$, the associated saddle connection complex A(S,q)$\mathcal A(S,q)$ is the simplicial complex where vertices are the saddle connections on (S,q)$(S,q)$, with simplices spanned by sets of pairwise disjoint saddle connections. This complex can be naturally reg...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
30 June 2022
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| In: |
Journal of topology
Year: 2022, Volume: 15, Issue: 3, Pages: 1248-1310 |
| ISSN: | 1753-8424 |
| DOI: | 10.1112/topo.12242 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1112/topo.12242 Verlag, lizenzpflichtig, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1112/topo.12242 
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| Author Notes: | Valentina Disarlo, Anja Randecker, Robert Tang |
| Summary: | For a half-translation surface (S,q)$(S,q)$, the associated saddle connection complex A(S,q)$\mathcal A(S,q)$ is the simplicial complex where vertices are the saddle connections on (S,q)$(S,q)$, with simplices spanned by sets of pairwise disjoint saddle connections. This complex can be naturally regarded as an induced subcomplex of the arc complex. We prove that any simplicial isomorphism ϕ:A(S,q)→A(S′,q′)$\phi \colon \mathcal A(S,q) \rightarrow \mathcal A(S^\prime ,q^\prime )$ between saddle connection complexes is induced by an affine diffeomorphism F:(S,q)→(S′,q′ |
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| Item Description: | Gesehen am 29.07.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1753-8424 |
| DOI: | 10.1112/topo.12242 |