## Topology & Geometric Group Theory Seminar

## Fall 2008

### 1:30 – 2:30, Malott 406

Tuesday, October 28

**Emanuele
Delucchi**, Binghamton University

*"Garside-type" models for complements of arrangements of
hyperplanes*

Bestvina's construction of a simplicial complex associated to any
finite type Artin group can be generalized to all complexified
arrangements of hyperplanes (i.e., beyond the arrangements of
reflecting hyperplanes of finite Coxeter groups). I will explain this
generalized construction, introducing the tools needed—namely
the Salvetti Complex and the "Homotopy colimits for combinatorial
applications" of Welker, Ziegler and Zivaljevic.

Aside from providing a natural setting for Deligne's theorem on
asphericity of complements of simplicial arrangements, this
construction raises interesting questions about the geometry and
combinatorics of "dual" Garside structures for finite-type Artin
groups and of Garside categories as studied by Bessis.

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