A lower bound on the number of homotopy types of simplicial complexes on n vertices

2018/04/18 by Newman, Andrew · 1 citation
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1804.06787

Abstract

For n ∈ ℕ, let h(n) denote the number of simplicial complexes on n vertices up to homotopy equivalence. Here we prove that h(n) ≥ 2^2^0.02n when n is large enough. Together with the trivial upper bound of 2²ⁿ on the number of labeled simplicial complexes on n vertices this proves a conjecture of Kalai that h(n) is doubly exponential in n.

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• Fundamental groups of small simplicial complexes

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