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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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Connectivity of a matroid is at least its rank?
The connectivity $\eta(X)$ of a simplicial complex $X$ is defined as the
$$1+\min_j\{j \mid \tilde{H}_j(X)\neq 0\}.$$
If no such $j$ exists, then $\eta(X):=\infty$.
(See here for this definition, whic …