Document Type
Article
Publication Date
1-1-2012
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 π1(Y) is free and H2(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
Publication Source (Journal or Book title)
Discrete and Computational Geometry
First Page
117
Last Page
149
Recommended Citation
Cohen, D., Costa, A., Farber, M., & Kappeler, T. (2012). Topology of Random 2-Complexes. Discrete and Computational Geometry, 47 (1), 117-149. https://doi.org/10.1007/s00454-011-9378-0