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- W2090464710 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." @default.
- W2090464710 created "2016-06-24" @default.
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- W2090464710 date "2011-10-21" @default.
- W2090464710 modified "2023-09-27" @default.
- W2090464710 title "Topology of Random 2-Complexes" @default.
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- W2090464710 doi "https://doi.org/10.1007/s00454-011-9378-0" @default.
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