2004/11/29 by David Bessis, Bessis, David · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.math/0411645
37 pages
arxiv created 2004/11/29 · arxiv updated 2009/12/01
Let V be a finite dimensional complex vector space and W⊂ \GL(V) be a finite complex reflection group. Let V\reg be the complement in V of the reflecting hyperplanes. A classical conjecture predicts that V\reg is a K(pi,1) space. When W is a complexified real reflection group, the conjecture follows from a theorem of Deligne. Our main result validates the conjecture for duality (or, equivalently, well-generated) complex reflection groups. This includes the complexified real case (but our proof is new) and new cases not previously known. We also address a number of questions about π1(W\cq V\reg), the braid group of W.