# Questions tagged [simplicial-complex]

A finite simplicial complex can be defined as a finite collection $K$ of simplices in $\mathbb{R}^N$ that satisfies the following conditions : (1) Any face of a simplex from $K$ is also in $K$ and (2) The intersection of any two simplices in $K$ is a face of both simplices.

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### (Reference Request) Simplicial Complexes and Homology Book

A student has asked for references on simplicial complexes, and I remember a book but can't find its name. Pretty sure it was a yellow Springer book, but not sure what series - and I'm not even 100% ...
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### Distances between two complexes when using Persistence Homology

I am using Persistence Homology to look at two different facebook networks. I can generate a distance matrix between individuals and then create the usual barcodes and persistence diagrams according ...
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### Not-matchings of a Hypergraph

I'd like to characterize the not-matchings of an hypergraph $H$, or more exactly its complements. A not-matching is a set of edges containing at least $2$ not-disjoint edges. If $H$ is a graph this ...
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### How many affine independent points could be found in $\mathbb R^n$?

I was reading about Simplicial Complexes definition in the book "Using the Borsuk–Ulam Theorem" and I confronted with affinely independent idea. So $$v_0,..., v_n$$ are affinely ...
### Computing the 0-dim cohomology group of a connected simplicial complex with coefficients in $\mathbb{Z}_{2}$
Let $L$ be a connected locally finite simplicial complex with coefficients in $\mathbb{Z}_{2}$. I want to prove that $H^{0}(L)=\mathbb{Z}_{2}$. We know that $H^{0}(L)$= \$Ker\delta_{1} / Im\delta_{0}=...