Stratified Morse Theory in Arrangements

Details Stratified Morse Theory in Arrangements Stratified Morse Theory in Arrangements

2006-03-20

arxiv.org/abs/math/0603471v1

Pure Appl. Math. Q. 2 (2006), 673-697

Mathematics

Algebraic Geometry

For Robert MacPherson on the occasion of his sixtieth birthday

Scientific paper

This paper is a survey of our work based on the stratified Morse theory of Goresky and MacPherson. First we discuss the Morse theory of Euclidean space stratified by an arrangement. This is used to show that the complement of a complex hyperplane arrangement admits a minimal cell decomposition. Next we review the construction of a cochain complex whose cohomology computes the local system cohomology of the complement of a complex hyperplane arrangement. Then we present results on the Gauss-Manin connection for the moduli space of arrangements of a fixed combinatorial type in rank one local system cohomology.

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