A 2-Person Game Decomposing 2-Manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912009741664256 |
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| author | Berman, David R. Leonard, Lee O. |
| author_facet | Berman, David R. Leonard, Lee O. |
| contents | Two players play a game by alternately splitting a surface of a compact $2$-manifold along a simple closed curve that is not null-homotopic and attaching disks to the resulting boundary; the last player who can move wins. Starting from an orientable surface, the $G$-series is $01\dot{2}\dot{0}$ according to increasing genus. Starting from a nonorientable surface, the $G$-series is $012\dot{4}60\dot{3}$ according to increasing genus. Nim addition determines the $G$-values of the remaining compact $2$-manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A 2-Person Game Decomposing 2-Manifolds Berman, David R. Leonard, Lee O. Combinatorics Geometric Topology Two players play a game by alternately splitting a surface of a compact $2$-manifold along a simple closed curve that is not null-homotopic and attaching disks to the resulting boundary; the last player who can move wins. Starting from an orientable surface, the $G$-series is $01\dot{2}\dot{0}$ according to increasing genus. Starting from a nonorientable surface, the $G$-series is $012\dot{4}60\dot{3}$ according to increasing genus. Nim addition determines the $G$-values of the remaining compact $2$-manifolds. |
| title | A 2-Person Game Decomposing 2-Manifolds |
| topic | Combinatorics Geometric Topology |
| url | https://arxiv.org/abs/2407.00816 |