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

2010/05/25 by Mikhail Grinberg, Grinberg, Mikhail
Computer Science · Mathematics · #32S50 #32S60 #Algebraic Geometry (math.AG) #Artificial Intelligence in Games #Complex Variables (math.CV) #FOS: Mathematics #Topological and Geometric Data Analysis #math.AG #math.CV #msc:32S50 #msc:32S60

paper · pdf · doi:10.48550/arxiv.1005.4488

31 pages

arxiv created 2010/05/25 · openalex publication_date 2010/05/25 · arxiv updated 2010/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Gradient-like vector fields on a complex analytic variety

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