Comparing combinatorial models of moduli space and their compactifications
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arXiv
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| Format: | Preprint |
| Published: |
2015
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| _version_ | 1866916218784448512 |
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| author | Santander, Daniela Egas Kupers, Alexander |
| author_facet | Santander, Daniela Egas Kupers, Alexander |
| contents | We compare two combinatorial models for the moduli space of two-dimensional cobordisms: Bödigheimer's radial slit configurations and Godin's admissible fat graphs, producing an explicit homotopy equivalence using a "critical graph" map. We also discuss natural compactifications of these two models, the unilevel harmonic compactification and Sullivan diagrams respectively, and prove that the homotopy equivalence induces a cellular homeomorphism between these compactifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_02725 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Comparing combinatorial models of moduli space and their compactifications Santander, Daniela Egas Kupers, Alexander Geometric Topology Algebraic Topology 32G15, 57M15, 57R56 We compare two combinatorial models for the moduli space of two-dimensional cobordisms: Bödigheimer's radial slit configurations and Godin's admissible fat graphs, producing an explicit homotopy equivalence using a "critical graph" map. We also discuss natural compactifications of these two models, the unilevel harmonic compactification and Sullivan diagrams respectively, and prove that the homotopy equivalence induces a cellular homeomorphism between these compactifications. |
| title | Comparing combinatorial models of moduli space and their compactifications |
| topic | Geometric Topology Algebraic Topology 32G15, 57M15, 57R56 |
| url | https://arxiv.org/abs/1506.02725 |