Steenbrink, J. H. M.; Stevens, J. Topological invariance of the weight filtration. (English) Zbl 0539.14016 Indag. Math. 46, 63-76 (1984). The paper addresses the problem: under which conditions is the weight filtration on the cohomology of a compact complex algebraic variety preserved under homeomorphisms? After a discussion of this question it is shown that the answer is always positive for compact algebraic surfaces (for quasi-projective surfaces the weight filtration is not even an analytic invariant). The proof uses the weight filtration on a neighborhood boundary of the singular locus, as introduced by A. H. Durfee [Duke Math. J. 50, 1017-1040 (1983)] and the topological structure of this 3-manifold [see W. D. Neumann, Trans. Am. Math. Soc. 268, 299-344 (1981)]. In particular, for isolated surface singularities the weight filtration on the cohomology of the link is a topological invariant. For higher dimensional singularities this is no longer true; examples are given of diffeomorphic links with different weight filtration. Cited in 6 Documents MSC: 14F45 Topological properties in algebraic geometry 14F25 Classical real and complex (co)homology in algebraic geometry Keywords:invariance of weight filtration on the cohomology under homeomorphisms; compact algebraic surfaces; isolated surface singularities PDFBibTeX XMLCite \textit{J. H. M. Steenbrink} and \textit{J. Stevens}, Indag. Math. 46, 63--76 (1984; Zbl 0539.14016)