Non-embeddability of geometric lattices and buildings
2014 (English)In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444, Vol. 51, no 4, 779-801 p.Article in journal (Refereed) Published
A fundamental question for simplicial complexes is to find the lowest dimensional Euclidean space in which they can be embedded. We investigate this question for order complexes of posets. We show that order complexes of thick geometric lattices as well as several classes of finite buildings, all of which are order complexes, are hard to embed. That means that such -dimensional complexes require -dimensional Euclidean space for an embedding. (This dimension is always sufficient for any -complex.) We develop a method to show non-embeddability for general order complexes of posets.
Place, publisher, year, edition, pages
2014. Vol. 51, no 4, 779-801 p.
Embedding, Buildings, Geometric lattice, Simplicial complex, Almost embedding, Finite projective space
IdentifiersURN: urn:nbn:se:kth:diva-140323DOI: 10.1007/s00454-014-9591-8ISI: 000337141000002ScopusID: 2-s2.0-84902269684OAI: oai:DiVA.org:kth-140323DiVA: diva2:689560
FunderKnut and Alice Wallenberg Foundation, KAW 2005.0098
Updated from "Submitted" to "Published". QC 201407072014-01-212014-01-212014-07-07Bibliographically approved