We study the isometry groups of compact spherical orientable 3-orbifolds S3/ G, where G is a finite subgroup of SO (4) , by determining their isomorphism type. Moreover, we prove that the inclusion of Isom(S3/G) into Diff(S3/G) induces an isomorphism of the π groups, thus proving the π-part of the natural generalization of the Smale Conjecture to spherical 3-orbifolds.
Isometry groups and mapping class groups of spherical 3-orbifolds
Seppi A.
2019-01-01
Abstract
We study the isometry groups of compact spherical orientable 3-orbifolds S3/ G, where G is a finite subgroup of SO (4) , by determining their isomorphism type. Moreover, we prove that the inclusion of Isom(S3/G) into Diff(S3/G) induces an isomorphism of the π groups, thus proving the π-part of the natural generalization of the Smale Conjecture to spherical 3-orbifolds.
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