Delucchi, Emanuele (2007) Nested set complexes of Dowling lattices and complexes of Dowling trees. Journal of Algebraic Combinatorics, 26 (4). pp. 477-494. ISSN 0925-9899
Full text not available from this repository.Abstract
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).
| Item Type: | Scientific journal article, Newspaper article or Magazine article |
|---|---|
| Subjects: | Mathematical sciences |
| Department/unit: | Dipartimento tecnologie innovative |
| Depositing User: | Emanuele Delucchi |
| Date Deposited: | 27 May 2022 08:22 |
| Last Modified: | 27 May 2022 14:00 |
| URI: | http://repository.supsi.ch/id/eprint/13404 |
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