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Homotopy theory, homological algebra, algebraic treatments of manifolds.

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 …
Michal Adamaszek's user avatar
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
Michal Adamaszek's user avatar
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 …
Michal Adamaszek's user avatar