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Results tagged with at.algebraic-topology
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user 120143
Homotopy theory, homological algebra, algebraic treatments of manifolds.
2
votes
Accepted
Homology of independence complex after removing a vertex
There is a fairly standard splitting technique as suggested in the comment, although not necessarily using $v$.
Let $G$ be a graph and $v$ is a simplicial vertex. Let $w$ be any neighbor of $v$. Then …
- 411
5
votes
Accepted
Amending flawed "proof" that homology groups are zero
Let $G_n$ be the graph with vertex set $\{2,\ldots,n\}$ in which there is an edge $ij$ if and only if $\mathrm{gcd}(i,j)>1$. The simplicial complex mentioned in Andy Putman's answer, as well as in you …
- 411
2
votes
0-1 matrix corresponding to an abstract simplicial complex
It might be that it is simply referred to as the vertex-facet incidence matrix, at least in some polytope papers like https://arxiv.org/pdf/math/0006225.pdf
- 411