Abstract
Let ( X, Y) be a polyhedral pair (see conventions) such that X is second countable. We give a relation between the homotopical depth of X along Y and the degree of connectivity of the pair ( X, X\\ Y) (a conjecture of Grothendieck). In particular, we obtain a relation between the rectified homotopical depth and the global rectified homotopical depth of a complex analytic space.
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