Change search
ReferencesLink to record
Permanent link

Direct link
Quotient complexes and lexicographic shellability
KTH, Superseded Departments, Mathematics.
2002 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 16, no 1, 83-96 p.Article in journal (Refereed) Published
Abstract [en]

Let Pi(n,k,k) and Pi(n,k,h), h < k, denote the intersection lattices of the k-equal subspace arrangement of type D-n and the k, h-equal subspace arrangement of type B-n respectively. Denote by S-n(B) the group of signed permutations. We show that Delta(Pi(n,k,k))/S-n(B) is collapsible. For Delta(Pi(n,k,h))/S-n(B),h < k, we show the following. If n = 0 (mod k), then it is homotopy equivalent to a sphere of dimension 2n/k = 2. If n = h (mod k), then it is homotopy equivalent to a sphere of dimension 2n-h/k-1. Otherwise, it is contractible. Immediate consequences for the multiplicity of the trivial characters in the representations of S-n(B) on the homology groups of Delta(Pi(n,k,k)) and Delta(Pi(n,k,h)) are stated. The collapsibility of Delta (Pi(n,k,k))/S-n(B) is established using a discrete Morse function. The same method is used to show that Delta(Pi(n,k,h))/S-n(B), h < k, is homotopy equivalent to a certain subcomplex. The homotopy type of this subcomplex is calculated by showing that it is shellable. To do this, we are led to introduce a lexicographic shelling condition for balanced cell complexes of boolean type. This extends to the non-pure case work of P. Hersh (Preprint, 2001) and specializes to the CL-shellability of A. Bjorner and M. Wachs (Trans. Amer. Math. Soc. 4 (1996), 1299-1327) when the cell complex is an order complex of a poset.

Place, publisher, year, edition, pages
2002. Vol. 16, no 1, 83-96 p.
Keyword [en]
quotient complex, cell complex of boolean type, lexicographic shellability, coxeter subspace arrangement, homotopy, subspace arrangements, simplicial posets
URN: urn:nbn:se:kth:diva-22002ISI: 000178886000006OAI: diva2:340700
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

Open Access in DiVA

No full text

Search in DiVA

By author/editor
Hultman, Axel
By organisation
In the same journal
Journal of Algebraic Combinatorics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 13 hits
ReferencesLink to record
Permanent link

Direct link