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Homotopical depth and a conjecture of Grothendieck. (Profondeur homotopique et conjecture de Grothendieck.) (French) Zbl 0978.55010
Let \((X,Y)\) be a polyhedral pair such that \(X\) is second countable. The author proves that the connectivity of the pair \((X,X \smallsetminus Y)\) is greater than or equal to \(-1\) plus the homotopical depth of \(X\) along \(Y\) (conjecture of Grothendieck). The paper contains also a relation between the rectified homological depth and the global rectified homotopical depth of a complex analytic space.

MSC:
55P99 Homotopy theory
32S20 Global theory of complex singularities; cohomological properties
57R19 Algebraic topology on manifolds and differential topology
Keywords:
analytic space
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