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Article Dans Une Revue Mathematische Zeitschrift Année : 2019

Isometry group and mapping class group of spherical 3-orbifolds

Résumé

We study the isometry group of compact spherical orientable 3-orbifolds S^3/G, where G is a finite subgroup of SO(4), by determining its isomorphism type and, when S^3/G is a Seifert fibrered orbifold, by describing the action on the Seifert fibrations induced by isometric copies of the Hopf fibration of S^3. Moreover, we prove that the inclusion of Isom(S^3/G) into Diff(S^3/G) induces an isomorphism of the π_0 groups, thus proving the π_0-part of the natural generalization of the Smale Conjecture to spherical 3-orbifolds.
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Dates et versions

hal-01474682 , version 1 (23-02-2017)

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Mattia Mecchia, Andrea Seppi. Isometry group and mapping class group of spherical 3-orbifolds. Mathematische Zeitschrift, 2019, 292.3, pp.1291-1314. ⟨10.1007/s00209-018-2166-2⟩. ⟨hal-01474682⟩
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