CW posets after the Poincare Conjecture

Patricia Hersh

CW posets after the Poincare Conjecture

Combinatorics 2014-11-06 v1

Authors: Patricia Hersh

Abstract

Anders Bjorner characterized which finite graded partially ordered sets arise as the posets of closure relations on cells of a finite, regular CW complex. His characterization of these "CW posets" required each open interval $(\hat{0},u)$ to have order complex homeomorphic to a sphere of dimension $rk(u)-2$ . Work of Danaraj and Klee showed that sufficient conditions were for the poset to be thin and shellable. The proof of the Poincare Conjecture enables the requirement of shellability to be replaced by the homotopy Cohen-Macaulay property. This expands the range of tools that may be used to prove a poset is a CW poset.

Keywords

partially ordered sets

Cite

@article{arxiv.1411.1296,
  title  = {CW posets after the Poincare Conjecture},
  author = {Patricia Hersh},
  journal= {arXiv preprint arXiv:1411.1296},
  year   = {2014}
}

Comments

I was recently encouraged to post this unpublished note from 2010 to the arXiv

CW posets after the Poincare Conjecture

Abstract

Keywords

Cite

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