Is there in the literature a list of three dimensional spherical, good orbifolds covered by nil, Sol and E3, and their algebraic topological invariants? (Homology, orbifold fundamental group).
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2$\begingroup$ I don't understand the question. You want the orbifolds to be a quotient of the sphere as orbifolds, but having nil- sol- and $E^3$ as the underlying manifolds? $\endgroup$– Igor RivinCommented Jan 10, 2018 at 19:40
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2$\begingroup$ @IgorRivin, surely it must be the other way round: orbifolds with underlying manifold the sphere (or perhaps spherical), but that arise as orbifold quotients of Nil, Sol or Euclidean manifolds? (Note that the orbifold fundamental group always surjects the fundamental group of the underlying space.) Anyway, hopefully the OP will clarify. $\endgroup$– HJRWCommented Jan 10, 2018 at 20:44
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1$\begingroup$ @HJRW That does make more sense, which does not prove that this is what the OP had meant :) $\endgroup$– Igor RivinCommented Jan 10, 2018 at 21:26
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1 Answer
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Yes, this was done by Bill Dunbar (for Euclidean orbifolds in his Princeton thesis, the general result is in an impossible to find 1988 paper:
Dunbar, William D., Geometric orbifolds, Rev. Mat. Univ. Complutense Madr. 1, No.1-3, 67-99 (1988). ZBL0655.57008.
answered Jan 10, 2018 at 21:40