Lectures on topology of complements and fundamental groups

2005/10/03 by Anatoly Libgober, Libgober, A.
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0510049

openalex publication_date 2005/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is an introduction to topology of complement to plane curves and hypersurfaces in the projective space and is based on the lectures given in Lumini in February and in ICTP (Trieste) in August of 2005. We discuss key problems concerning the families of singular curves, the one variable Alexander polynomials and the module over ring of Laurent polynomials structure on the homotopy groups of the complements to hypersurfaces with isolated singularities. We also discuss multivariable generalizations of these invariants and the Hodge theory of infinite abelian covers used in calculations of multivariable invariants. A historical overview is included as the opening section

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