×

Weak Lefschetz and topological \(q\)-completeness. (English) Zbl 0853.57024

Brasselet, Jean-Paul (ed.), Singularities. Papers of the international congress ‘Singularities in geometry and topology’, held in Lille (France), 3-8 June, 1991. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 201, 175-210 (1994).
Summary: Let \(\iota: A\hookrightarrow X\) denote the inclusion mapping of a closed complex subspace of a complex analytic space \(X\). The Weak Lefschetz Theorem deals with the question to what extent the induced homomorphisms in homology (with closed supports if \(X\) is not compact) or intersection cohomology are bijective. Our answer uses the degree of topological completeness of \(X\smallsetminus A\), an invariant that facilitates the reduction of relative to absolute situations. See 5.1 for an absolute and 5.2, 5.11, 5.7, and 8.3 for relative homological results, moreover 6.1 and 8.3 for intersection cohomology.
For the entire collection see [Zbl 0796.00018].

MSC:

57R19 Algebraic topology on manifolds and differential topology
32C99 Analytic spaces
PDFBibTeX XMLCite