The authors construct a de Rham-type Kasparov cycle for groups acting on CAT(0)-cubical spaces and use it to reprove Baum-Connes with coefficients for these groups.
Isometries of CAT(0) cube complexes are semi-simple
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abstract
We show that an automorphism of an arbitrary CAT(0) cube complex either has a fixed point or preserves some combinatorial axis. It follows that when a group contains a distorted cyclic subgroup, it admits no proper action on a discrete space with walls.
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2019 1verdicts
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On the Baum-Connes Conjecture for Groups Acting on CAT(0)-Cubical Spaces
The authors construct a de Rham-type Kasparov cycle for groups acting on CAT(0)-cubical spaces and use it to reprove Baum-Connes with coefficients for these groups.