2002/10/03 by Dmitry N. Kozlov
Mathematics · #math.GN #math.AT #math.CO #msc:57Q05 #msc:05C05 #msc:58K15
published as Discrete Comput. Geom. 32 (2004), no. 3, 373--382.
arxiv created 2002/10/03 · arxiv updated 2009/11/30
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.