Dimensions of the Ascending and Descending Sets in Complex Stratified Morse Theory
Algebraic Geometry
2010-05-26 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.1005.4488,
title = {Dimensions of the Ascending and Descending Sets in Complex Stratified Morse Theory},
author = {Mikhail Grinberg},
journal= {arXiv preprint arXiv:1005.4488},
year = {2010}
}
Comments
31 pages