The arc complexes of partially decorated hyperbolic polygons
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909504479690752 |
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| author | Panda, Pallavi |
| author_facet | Panda, Pallavi |
| contents | We consider two families of hyperbolic polygons: ideal and ideal once-punctured, some of whose spikes are decorated with horoballs. We show that the arc complexes of these two families of surfaces, generated by edge-to-edge arcs and edge-to-decorated-spike arcs, are closed piecewise linear balls. This is proved in a completely combinatorial setting: compact polygons whose vertices are assigned red or blue colouring. In order to prove the ballness, we show that these simplicial complexes are pseudo-manifolds and use shellability to conclude. As a consequence, we parametrise weakly-lengthening deformations of the partially decorated hyperbolic polygons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06695 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The arc complexes of partially decorated hyperbolic polygons Panda, Pallavi Combinatorics Geometric Topology 53A35, 57Q05 We consider two families of hyperbolic polygons: ideal and ideal once-punctured, some of whose spikes are decorated with horoballs. We show that the arc complexes of these two families of surfaces, generated by edge-to-edge arcs and edge-to-decorated-spike arcs, are closed piecewise linear balls. This is proved in a completely combinatorial setting: compact polygons whose vertices are assigned red or blue colouring. In order to prove the ballness, we show that these simplicial complexes are pseudo-manifolds and use shellability to conclude. As a consequence, we parametrise weakly-lengthening deformations of the partially decorated hyperbolic polygons. |
| title | The arc complexes of partially decorated hyperbolic polygons |
| topic | Combinatorics Geometric Topology 53A35, 57Q05 |
| url | https://arxiv.org/abs/2306.06695 |