Determination up to isomorphism of right-angled Coxeter systems. (English) Zbl 1054.20021
Summary: We announce that every right-angled Coxeter group determines its Coxeter system up to isomorphism. This implies that Dranishnikov’s rigidity conjecture holds for right-angled Coxeter groups, i.e., every right-angled Coxeter group determines its boundary up to homeomorphism.
MSC:
| 20F55 | Reflection and Coxeter groups (group-theoretic aspects) |
| 20F65 | Geometric group theory |
| 57M07 | Topological methods in group theory |
Keywords:
right-angled Coxeter groups; Coxeter systems; Dranishnikov rigidity conjecture; boundaries of groupsReferences:
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