Orbifold morse-smale-witten complexes

Cheol Hyun Cho, Hansol Hong

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Given a Morse-Smale function on an effective orientable orbifold, we construct its Morse-Smale-Witten complex. We show that critical points of a certain type have to be discarded to build a complex properly, and that gradient flows should be counted with suitable weights. Its homology is proven to be isomorphic to the singular homology of the quotient space under the self-indexing assumption. For a global quotient orbifold [M/G], such a complex can be understood as the G-invariant part of the Morse complex of M, where the G-action on generators of the Morse complex has to be defined including orientation spaces of unstable manifolds at the critical points. Alternatively in the case of global quotients, we introduce the notion of weak group actions on Morse-Smale-Witten complexes for non-invariant Morse-Smale functions on M, which give rise to genuine group actions on the level of homology.

Original languageEnglish
Article number1450040
JournalInternational Journal of Mathematics
Volume25
Issue number5
DOIs
Publication statusPublished - 2014 Jan 1

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Orbifold
Homology
Group Action
Critical point
Quotient
Unstable Manifold
Quotient Space
Gradient Flow
Indexing
Isomorphic
Generator
Invariant

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Orbifold morse-smale-witten complexes. / Cho, Cheol Hyun; Hong, Hansol.

In: International Journal of Mathematics, Vol. 25, No. 5, 1450040, 01.01.2014.

Research output: Contribution to journalArticle

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