The smale conjecture for seifert fibered spaces with hyperbolic base orbifold

Darryl McCullough University of Oklahoma Teruhiko Soma Tokyo Metropolitan University

Differential Geometry mathscidoc:1609.10301

Journal of Differential Geometry, 93, (2), 327-353, 2013
Let M be a closed orientable 3-manifold admitting an H2 × R or gSL2(R) geometry, or equivalently a Seifert fibered space with a hyperbolic base 2-orbifold. 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 S1, according as the center of 1(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 SF(M) for compact orientable aspherical 3-manifolds. We also prove that when M has an H2×R or gSL2(R) geometry and the base orbifold has underlying manifold the 2sphere with three cone points, the inclusion Isom(M) ! Diff(M) is a homotopy equivalence.
No keywords uploaded!
[ Download ] [ 2016-09-14 07:40:37 uploaded by admin ] [ 668 downloads ] [ 0 comments ] [ Cited by 6 ]
@inproceedings{darryl2013the,
  title={THE SMALE CONJECTURE FOR SEIFERT FIBERED SPACES WITH HYPERBOLIC BASE ORBIFOLD},
  author={Darryl McCullough, and Teruhiko Soma},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914074037378422963},
  booktitle={Journal of Differential Geometry},
  volume={93},
  number={2},
  pages={327-353},
  year={2013},
}
Darryl McCullough, and Teruhiko Soma. THE SMALE CONJECTURE FOR SEIFERT FIBERED SPACES WITH HYPERBOLIC BASE ORBIFOLD. 2013. Vol. 93. In Journal of Differential Geometry. pp.327-353. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914074037378422963.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved