Orbifold Morse-Smale-Witten complex
Algebraic Topology
2018-05-31 v3 Symplectic Geometry
Abstract
We construct Morse-Smale-Witten complex for an effective orientable orbifold. For a global quotient orbifold, we also construct a Morse-Bott complex. We show that certain type of critical points of a Morse function has to be discarded to construct such a complex, and gradient flows should be counted with suitable weights. The homology of these complexes are shown to be isomorphic to the singular homology of the quotient spaces under the self-indexing assumptions.
Keywords
Cite
@article{arxiv.1103.5528,
title = {Orbifold Morse-Smale-Witten complex},
author = {Cheol-Hyun Cho and Hansol Hong},
journal= {arXiv preprint arXiv:1103.5528},
year = {2018}
}
Comments
35 pages, 6 figures; The content of the last section is replaced by the explanation on weak group actions. Some other minor changes