Dimensions of the Ascending and Descending Sets in Complex Stratified Morse Theory

Details Dimensions of the Ascending and Descending Sets in Complex Stratified Morse Theory Dimensions of the Ascending and Descending Sets in Complex Stratified Morse Theory

2010-05-25

arxiv.org/abs/1005.4488v1

Mathematics

Algebraic Geometry

31 pages

Scientific paper

We present a new construction of gradient-like vector fields in the setting of Morse theory on a complex analytic stratification. We prove that the ascending and descending sets for these vector fields possess cell decompositions satisfying the dimension bounds conjectured by M. Goresky and R. MacPherson. Similar results by C.-H. Cho and G. Marelli have recently appeared in arXiv:0908.1862.

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