10
votes
0answers
374 views

Has this chain complex associated with a simplicial complex been studied before?

I have stumbled upon a construction that has probably been noticed before, and I wonder if anyone can point me to a reference. Suppose that $K$ is a simplicial complex. Let $P(K)$ be the free abelian ...
-1
votes
1answer
69 views

Poset complex of reverse ordering [closed]

This might be too easy but I cannot proof it easily. Any reference or hint will be great. Q: Suppose P is a poset in which every chain is finite and $\Delta P$ is the poset complex associated to it. ...
5
votes
1answer
261 views

Does every simplicial polytope have a topology-preserving contractible edge?

An edge of a triangulated manifold is said to be contractible if it may be contracted to a vertex without modifying the topological type of the underlying manifold. Otherwise, the edge is ...
3
votes
0answers
172 views

Simplicial chain complex with ordered simplices

Let $X$ be an abstract simplicial complex. Recall that the usual simplicial chain complex for $X$ is defined as follows. Let $C_k(X)$ be the quotient of the free abelian group on formal symbols ...
7
votes
2answers
360 views

Combinatorial distance between simplicial complexes

Let $K_1$ and $K_2$ be two simplicial complexes. I am seeking a measure of the distance between $K_1$ and $K_2$ when viewed as combinatorial objects. What I have in mind is something like this. ...
1
vote
0answers
103 views

Do bistellar flips in a simplicial sphere preserve facet connectivity?

Define two facets of a simplicial sphere as k-connected if there are at least k disjoint edge-vertex paths between them in their facet-ridge graphs. Do bistellar flips preserve facet k-connectivity? ...