Nested set complexes of Dowling lattices and complexes of Dowling trees
| dc.creator | Delucchi, Emanuele | |
| dc.date | 2006-03-15 | |
| dc.date | 2006-11-14 | |
| dc.date.accessioned | 2026-07-07T07:06:57Z | |
| dc.date.available | 2026-07-07T07:06:57Z | |
| dc.description | 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 Q_G which was recently introduced by Hultman together with the complex of G-symmetric phylogenetic trees T_G. Hultman shows that T_G and Q_G 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 T_G is subdivided by the order complex of Q_G. We introduce the complex of Dowling trees T(G) and prove that it is subdivided by the order complex of Q(G) and contains T_G as a subcomplex. We show that T(G) is obtained from T_G by successive coning over certain subcomplexes. We explicitly and independently calculate how many homology spheres are added in passing from T_G to T(G). | |
| dc.description | 14 pages, 2 figures, corrected typos, added references | |
| dc.identifier | https://arxiv.org/abs/math/0603383 | |
| dc.identifier | http://arxiv.org/abs/math/0603383 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110213 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | 37F20 | |
| dc.title | Nested set complexes of Dowling lattices and complexes of Dowling trees | |
| dc.type | text |