The Library
Topology of random 2-complexes
Tools
Cohen, D., Costa, A., Farber, Michael and Kappeler, T. (2012) Topology of random 2-complexes. Discrete & Computational Geometry, Vol.47 (No.1). pp. 117-149. doi:10.1007/s00454-011-9378-0 ISSN 0179-5376.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1007/s00454-011-9378-0
Abstract
We study the Linial–Meshulam model of random two-dimensional simplicial complexes. One of our main results states that for p≪n −1 a random 2-complex Y collapses simplicially to a graph and, in particular, the fundamental group π 1(Y) is free and H 2(Y)=0, asymptotically almost surely. Our other main result gives a precise threshold for collapsibility of a random 2-complex to a graph in a prescribed number of steps. We also prove that, if the probability parameter p satisfies p≫n −1/2+ϵ , where ϵ>0, then an arbitrary finite two-dimensional simplicial complex admits a topological embedding into a random 2-complex, with probability tending to one as n→∞. We also establish several related results; for example, we show that for p<c/n with c<3 the fundamental group of a random 2-complex contains a non-abelian free subgroup. Our method is based on exploiting explicit thresholds (established in the paper) for the existence of simplicial embeddings and immersions of 2-complexes into a random 2-complex.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Discrete & Computational Geometry | ||||
Publisher: | Springer New York LLC | ||||
ISSN: | 0179-5376 | ||||
Official Date: | January 2012 | ||||
Dates: |
|
||||
Volume: | Vol.47 | ||||
Number: | No.1 | ||||
Page Range: | pp. 117-149 | ||||
DOI: | 10.1007/s00454-011-9378-0 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |