Directed trees in a string, real polynomials with triple roots, and chain mails
General Topology
2007-05-23 v1 Algebraic Topology
Combinatorics
Abstract
This paper starts with an observation that two infinite series of simplicial complexes, which a priori do not seem to have anything to do with each other, have the same homotopy type. One series consists of the complexes of directed forests on a double directed string, while the other one consists of Shapiro-Welker models for the spaces of hyperbolic polynomials with a triple root. We explain this coincidence in the more general context by finding an explicit homotopy equivalence between complexes of directed forests on a double directed tree, and doubly disconnecting complexes of a tree.
Keywords
Cite
@article{arxiv.math/0210045,
title = {Directed trees in a string, real polynomials with triple roots, and chain mails},
author = {Dmitry N. Kozlov},
journal= {arXiv preprint arXiv:math/0210045},
year = {2007}
}