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arXiv · 1710.02063

Connectivity Properties of Factorization Posets in Generated Groups

Henri Mühle·Vivien Ripoll
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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.

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Henri Mühle, Vivien Ripoll. 2017-10-05. Connectivity Properties of Factorization Posets in Generated Groups. https://doi.org/10.1007/s11083-019-09496-1

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