2006/03/15 by Emanuele Delucchi, Delucchi, Emanuele
Chemistry · Computer Science · Mathematics · #37F20 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Topological and Geometric Data Analysis #math.AT #math.CO #msc:37F20
paper · pdf · doi:10.48550/arxiv.math/0603383
14 pages, 2 figures, corrected typos, added references
openalex publication_date 2006/03/15 · arxiv created 2006/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice Q(G) and of its subposet of the G-symmetric partitions QG which was recently introduced by Hultman together with the complex of G-symmetric phylogenetic trees TG. Hultman shows that TG and QG are homotopy equivalent and Cohen-Macaulay, and determines the rank of their top homology. An application of the theory of building sets and nested set complexes by Feichtner and Kozlov shows that in fact TG is subdivided by the order complex of QG. We introduce the complex of Dowling trees T(G) and prove that it is subdivided by the order complex of Q(G) and contains TG as a subcomplex. We show that T(G) is obtained from TG by successive coning over certain subcomplexes. We explicitly and independently calculate how many homology spheres are added in passing from TG to T(G).