Sharp vanishing thresholds for cohomology of random flag complexes
From MaRDI portal
Publication:2453590
DOI10.4007/annals.2014.179.3.5zbMath1294.05195arXiv1207.0149OpenAlexW2963188634MaRDI QIDQ2453590
Publication date: 10 June 2014
Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1207.0149
Random graphs (graph-theoretic aspects) (05C80) Planar graphs; geometric and topological aspects of graph theory (05C10) Combinatorial aspects of simplicial complexes (05E45)
Related Items
The threshold for integer homology in random \(d\)-complexes ⋮ Limit theory for U-statistics under geometric and topological constraints with rare events ⋮ Topology of random geometric complexes: a survey ⋮ Inverse expander mixing for hypergraphs ⋮ Topology of clique complexes of line graphs ⋮ Random Simplicial Complexes: Models and Phenomena ⋮ Exponential random simplicial complexes ⋮ Random simplicial complexes, duality and the critical dimension ⋮ Homological connectivity in random Čech complexes ⋮ Phase transition in cohomology groups of non-uniform random simplicial complexes ⋮ Random graph products of finite groups are rational duality groups ⋮ On the spectrum of dense random geometric graphs ⋮ On the contractibility of random Vietoris-Rips complexes ⋮ Random Čech complexes on manifolds with boundary ⋮ Law of large numbers for Betti numbers of homogeneous and spatially independent random simplicial complexes ⋮ Homology of multi-parameter random simplicial complexes ⋮ What Are Higher-Order Networks? ⋮ Random hypergraphs, random simplicial complexes and their Künneth-type formulae ⋮ One‐sided sharp thresholds for homology of random flag complexes ⋮ Edge ideals of Erdős-Rényi random graphs: linear resolution, unmixedness and regularity ⋮ The regularity of almost all edge ideals ⋮ Random Simplicial Complexes ⋮ Random Čech complexes on Riemannian manifolds ⋮ Random toric surfaces and a threshold for smoothness ⋮ Thresholds for vanishing of `isolated' faces in random Čech and Vietoris-Rips complexes ⋮ Betti numbers of complexes with highly connected links ⋮ Random flag complexes and asymptotic syzygies ⋮ Spectral gap bounds for the simplicial Laplacian and an application to random complexes ⋮ Asymptotics of integrals of Betti numbers for random simplicial complex processes ⋮ Limit theorems for topological invariants of the dynamic multi-parameter simplicial complex ⋮ Evaluating visual properties via robust HodgeRank ⋮ Random walks on simplicial complexes and harmonics ⋮ Asymptotic behavior of lifetime sums for random simplicial complex processes ⋮ The Why, How, and When of Representations for Complex Systems ⋮ Convergence of persistence diagram in the sparse regime ⋮ Collapsibility of random clique complexes
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the triangle space of a random graph
- Topology of random 2-complexes
- Enumeration of \({\mathbb{Q}}\)-acyclic simplicial complexes
- Homological connectivity of random 2-complexes
- Topology of random clique complexes
- On \(L^2\)-cohomology and property (T) for automorphism groups of polyhedral cell complexes
- Property (T) and Kazhdan constants for discrete groups
- A user's guide to discrete Morse theory
- p-adic curvature and the cohomology of discrete subgroups of p-adic groups
- Eigenvalues and homology of flag complexes and vector representations of graphs
- The variation of the spectrum of a normal matrix
- Groupes d'homotopie et classes de groupes abéliens
- The threshold function for vanishing of the top homology group of random 𝑑-complexes
- The fundamental group of random 2-complexes
- Homological connectivity of random k -dimensional complexes
- A Random Graph With a Subcritical Number of Edges
- COBOUNDARY EXPANDERS
- When does the top homology of a random simplicial complex vanish?