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arXiv · 2407.00816

A 2-Person Game Decomposing 2-Manifolds

David R. Berman·Lee O. Leonard
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Abstract

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.

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David R. Berman, Lee O. Leonard. 2024-09-02. A 2-Person Game Decomposing 2-Manifolds. https://arxiv.org/abs/2407.00816

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