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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