Mathematics – Algebraic Topology
Scientific paper
2000-05-24
Mathematics
Algebraic Topology
Scientific paper
In this paper we study various simplicial complexes associated to the commutative structure of a finite group G. We define NC(G) (resp. C(G)) as the complex associated to the poset of pairwise non-commuting (resp. commuting) sets in G. We observe that NC(G) has only one positive dimensional connected component, which we call BNC(G), and we prove that BNC(G) is simply connected. Our main result is a simplicial decomposition formula for BNC(G) which follows from a result of A. Bjorner, M. Wachs and V. Welker on inflated simplicial complexes. As a corollary, we obtain that if G has a nontrivial center or if G has odd order, then the homology group H_{n-1}(BNC(G)) is nontrivial for every n such that G has a maximal noncommuting set of order n.
Pakianathan Jonathan
Yalçin Ergün
No associations
LandOfFree
On commuting and non-commuting complexes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On commuting and non-commuting complexes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On commuting and non-commuting complexes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-99131