Fixed point theorems for actions of Coxeter groups on nonpositively curved singular spaces.

摘要

We consider global fixed points for actions of Coxeter groups on nonpositively curved singular spaces. In particular, we characterize dimensional restrictions for the existence of nontrivial actions on CAT(0) spaces in terms of an easily verifiable condition on the Coxeter presentation. This has applications to irreducible representations and to complex of groups decompositions of Coxeter groups.