The Smale Conjecture for Hyperbolic 3-Manifolds: Isom (M3) ≃ Diff (M3)

Supersymmetric M3-branes and G 2 Manifolds

We obtain a generalisation of the original complete Ricci-flat metric of G 2 holonomy on R 4 × S 3 to a family with a non-trivial parameter λ. For generic λ the solution is singular, but it is regular when λ = {−1, 0, +1}. The case λ = 0 corresponds to the original G 2 metric, and λ = {−1, 1} are related to this by an S 3 automorphism of the SU (2) 3 isometry group that acts on the S 3 × S 3 pr...

The Generalized Smale Conjecture for 3-manifolds with Genus 2 One-sided Heegaard Splittings

The Generalized Smale Conjecture asserts that the inclusion of the group of isometries of any closed 3-manifold of constant positive curvature into the group of all its diffeomorphisms is a homotopy equivalence. In this paper, the conjecture is proven for all such 3-manifolds that contain a one-sided Klein bottle, except for the lens

Selective Dependence of H2-M3

Geometric models for hyperbolic 3-manifolds

In [Mi4,BrocCM1], Minsky, Brock and Canary gave a proof of Thurston’s Ending Lamination Conjecture for indecomposable hyperbolic 3-manifolds. In this paper, we offer another approach to this which was inspired by the original. Many of the key results are similar, though the overall logic is somewhat different. A possible advantage is that much of the relevant theory of “hierarchies” and other, ...

Horocycles in hyperbolic 3-manifolds