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arXiv · 2410.15276

The Pants Graph of a Free Group

Donggyun Seo
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Abstract

We introduce the concept of a pants decomposition for a finitely generated free group and construct the corresponding pants graph. A pants decomposition of a free group leads to the formation of a simplicial graph, referred to as the pants graph of a free group, consisting of all possible pants decompositions. The natural isometric action of the outer automorphism group of the free group on the pants graph induces a coarsely surjective orbit map. Additionally, we construct a coarsely Lipschitz map from the pants graph to the free splitting complex. These results imply that the pants graph of a free group is both connected and unbounded.

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Donggyun Seo. 2024-10-20. The Pants Graph of a Free Group. https://doi.org/10.1112/topo.70078

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