Connectivity Properties of Factorization Posets in Generated Groups

Abstract

We consider three notions of connectivity and their interactions in partially ordered sets coming from reduced factorizations of an element in a generated group. While one form of connectivity essentially reflects the connectivity of the poset diagram, the other two are a bit more involved: Hurwitz-connectivity has its origins in algebraic geometry, and shellability in topology. We propose a framework to study these connectivity properties in a uniform way. Our main tool is a certain linear order of the generators that is compatible with the chosen element.

35 pages, 17 figures. Comments are very welcome. Final version

References in corpus (1)

• A Poset Structure on the Alternating Group Generated by 3-Cycles

Cited by in corpus (2)

• A Poset Structure on the Alternating Group Generated by 3-Cycles
• In which it is proven that, for each parabolic quasi-Coxeter element in a finite real reflection group, the orbits of the Hurwitz action on its reflection factorizations are distinguished by the two obvious invariants