2010/05/27 by Darryl McCullough, McCullough, Darryl, Teruhiko Soma +1
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1005.5061
openalex publication_date 2010/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a closed orientable Seifert fibered 3-manifold with a hyperbolic base 2-orbifold, or equivalently, admitting a geometry modeled on H2 × 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.