Bordifications of hyperplane arrangement complements and curve complexes of spherical Artin groups

Abstract: The complement of an arrangement of hyperplanes in a complex vector space has a natural bordification to a manifold with corners formed by removing tubular neighborhoods of the hyperplanes and certain of their intersections. When the arrangement is the complexification of a real simplicial arrangement, the bordification closely resembles Harvey's bordification of the braid group. The faces of the universal cover of the bordification are parameterized by the simplices of a simplicial complex, the vertices of which are the irreducible ``parabolic subgroups'' of the fundamental group of the arrangement complement. When the arrangement is associated to a finite reflection group, we get the "curve complex" of the associated pure Artin group. In analogy with curve complexes for mapping class groups and with spherical buildings, our curve complex has the homotopy type of a wedge of spheres. This is joint work with Jingyin Huang.

algebraic topologydifferential geometrygeneral topologygroup theorygeometric topology

Audience: researchers in the topic

Ohio State Topology and Geometric Group Theory Seminar

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