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Dimensions of the Ascending and Descending Sets in Complex Stratified Morse Theory (1005.4488v1)
Published 25 May 2010 in math.AG and math.CV
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.
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