TY - JOUR
T1 - Determination of the topological structure of an orbifold by its group of orbifold diffeomorphisms
AU - Borzellino, Joseph E.
AU - Brunsden, Victor
PY - 2003/1/1
Y1 - 2003/1/1
N2 - 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.
AB - 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.
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M3 - Article
AN - SCOPUS:0041360162
SN - 0949-5932
VL - 13
SP - 311
EP - 327
JO - Journal of Lie Theory
JF - Journal of Lie Theory
IS - 2
ER -