Stratified Picard-Lefschetz Theory with Twisted Coefficients
Victor A. Vassiliev
TL;DR
This paper investigates the monodromy action on the homology of complements of stratified complex varieties with twisted coefficients, extending Picard-Lefschetz theory to stratified Morse singularities.
Contribution
It generalizes Picard-Lefschetz formulas to stratified settings with twisted coefficients, linking local monodromy to transversal slices of strata.
Findings
Reduction of local monodromy operators to transversal slices
Extension of Picard-Lefschetz formulas to stratified varieties
Application to stratified Morse singularities
Abstract
The monodromy action in the homology (generally with twisted coefficients) of complements of stratified complex analytic varieties depending on parameters is studied. For a wide class of local degenerations of such families (stratified Morse singularities) local monodromy and variation operators are reduced to similar operators acting in the transversal slices of corresponding strata. In particular, these results imply a main part of F. Pham's generalized Picard--Lefschetz formulae.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models