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The goal of this chapter is to prove Theorem 13.4.1 which asserts that any Coxeter group of type \(\mathrm {PM}\) is strongly rigid. Roughly,“type \(\mathrm {PM}\) ” means the nerve of \((W,S)\) is an orientable pseudomanifold. “Strongly rigid” means any two fundamental sets of generators for W are conjugate.

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Rigidity

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  • 发表日期：

    2025年

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  • Michael W. Davis

摘要

The goal of this chapter is to prove Theorem 13.4.1 which asserts that any Coxeter group of type \(\mathrm {PM}\) is strongly rigid. Roughly,“type \(\mathrm {PM}\) ” means the nerve of \((W,S)\) is an orientable pseudomanifold. “Strongly rigid” means any two fundamental sets of generators for W are conjugate.