Geometrically constructed bases for homology of partition lattices of types A, B and D
| dc.creator | Björner, Anders | |
| dc.creator | Wachs, Michelle L. | |
| dc.date | 2004-01-02 | |
| dc.date.accessioned | 2026-07-07T05:04:20Z | |
| dc.date.available | 2026-07-07T05:04:20Z | |
| dc.description | We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types A, B and D. This extends and explains the "splitting basis" for the homology of the partition lattice given in [Wa96], thus answering a question asked by R. Stanley. More explicitly, the following general technique is presented and utilized. Let A be a central and essential hyperplane arrangement in R^d. Let R_1,...,R_k be the bounded regions of a generic hyperplane section of A. We show that there are induced polytopal cycles ρ_{R_i} in the homology of the proper part \bar{L_A} of the intersection lattice such that {ρ_{R_i}}_{i=1,...,k} is a basis for \tilde H_{d-2}(\bar{L_A}). This geometric method for constructing combinatorial homology bases is applied to the Coxeter arrangements of types A, B and D, and to some interpolating arrangements. | |
| dc.description | 29 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/math/0401006 | |
| dc.identifier | http://arxiv.org/abs/math/0401006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69762 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E25; 52C35; 52C40 | |
| dc.title | Geometrically constructed bases for homology of partition lattices of types A, B and D | |
| dc.type | text |