Orbifold Morse-Smale-Witten complex

Details Orbifold Morse-Smale-Witten complex Orbifold Morse-Smale-Witten complex

2011-03-29

arxiv.org/abs/1103.5528v2

Mathematics

Algebraic Topology

28 pages, 3 figures

Scientific paper

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.

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