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

Joseph E. Borzellino, Victor Brunsden

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 - Jan 1 2003

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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