Determination of the topological structure of an orbifold by its group of orbifold diffeomorphisms

Joseph E. Borzellino, Victor W. Brunsden

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We show that the topological structure of a compact, locally smooth orbifold is determined by its orbifold diffeomorphism group. Let Diff Orbr(O) denote the Cr orbifold diffeomorphisms of an orbifold O. Suppose that Φ: DiffOrbr(O 1) → DiffOrbr(O2) is a group isomorphism between the the orbifold diffeomorphism groups of two orbifolds O1 and O2. We show that Φ is induced by a homeomorphism h: XO1 → XO2, where XO denotes the underlying topological space of O. That is, Φ(f) = hfh -1 for all f ∈ DiffOrbr(O1). Furthermore, if r > 0, then h is a Cr manifold diffeomorphism when restricted to the complement of the singular set of each stratum.

Original languageEnglish (US)
Pages (from-to)311-327
Number of pages17
JournalJournal of Lie Theory
Volume13
Issue number2
StatePublished - 2003

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Orbifold
Topological Structure
Diffeomorphisms
Diffeomorphism Group
Denote
CR Manifold
Singular Set
Diffeomorphism
Locally Compact
Homeomorphism
Topological space
Isomorphism
Complement

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Determination of the topological structure of an orbifold by its group of orbifold diffeomorphisms. / Borzellino, Joseph E.; Brunsden, Victor W.

In: Journal of Lie Theory, Vol. 13, No. 2, 2003, p. 311-327.

Research output: Contribution to journalArticle

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