The Smale conjecture for Seifert fibered spaces with hyperbolic base orbifold

Details The Smale conjecture for Seifert fibered spaces with hyperbolic base orbifold The Smale conjecture for Seifert fibered spaces with hyperbolic base orbifold

2010-05-27

arxiv.org/abs/1005.5061v1

Mathematics

Geometric Topology

Scientific paper

Let M be a closed orientable Seifert fibered 3-manifold with a hyperbolic base 2-orbifold, or equivalently, admitting a geometry modeled on H^2 \times R or the universal cover of SL(2,R). Our main result is that the connected component of the identity map in the diffeomorphism group Diff(M) is either contractible or homotopy equivalent to the circle, according as the center of the fundamental group of M is trivial or infinite cyclic. Apart from the remaining case of non-Haken infranilmanifolds, this completes the homeomorphism classifications of Diff(M) and of the space of Seifert fiberings of M for all compact orientable aspherical 3-manifolds. We also prove that when the base orbifold of M is hyperbolic with underlying manifold the 2-sphere with three cone points, the inclusion from the isometry group Isom(M) to Diff(M) is a homotopy equivalence.

Affiliated with

Also associated with

No associations

Rating

The Smale conjecture for Seifert fibered spaces with hyperbolic base orbifold does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Smale conjecture for Seifert fibered spaces with hyperbolic base orbifold, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Smale conjecture for Seifert fibered spaces with hyperbolic base orbifold will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-192393