This page is for a seminar on mapping class groups of 3-dimensional manifolds at the University of Glasgow during the academic year 2023 - 4.
Here is the schedule of talks and their topics.
The aim is to survey what is known about these mapping class groups, to understand the main ideas that go into the proofs.
The hope is that participants will be equipped to be able to compute the mapping class group of any 3-manifold that arises in their work.
The organisers are Rachael Boyd and Mark Powell.
Contact details:
rachael.boyd@glasgow.ac.uk
mark.powell@glasgow.ac.uk
General resources on 3-manifolds.
3-manifolds by J. Hempel.
Notes on basic 3-manifold topology by A. Hatcher.
The classification of 3-manifolds - a brief overview by A. Hatcher.
3-manifold groups by M. Aschenbrenner, S. Friedl, and H. Wilton.
Geometries of 3-manifolds by P. Scott.
Lectures on three-manifold topology by W. Jaco.
Sur les 2-sphères d'une variété de dimension 3 by F. Laudenbach.
Topologie de la dimension trois homotopie et isotopie by F. Laudenbach.
Finiteness of classifying spaces of relative diffeomorphism groups of 3-manifolds by A. Hatcher and D. McCullough.
Mapping class groups of 3-manifolds then and now by S. Hong and D. McCullough.
The 3-sphere.
Sur les difféomorphismes de la sphère de dimension trois by J. Cerf.
Eliashberg's proof of Cerf's theorem by H. Geiges and K. Zehmisch.
About the diffeomorphisms of the 3-sphere and a famous theorem of Cerf by F. Laudenbach.
A proof of the Smale conjecture by A. Hatcher.
Linearization in 3-manifold topology by A. Hatcher (1978 ICM talk).
Hatcher's proof of the Smale conjecture by A. Amabel.
Heegaard genus one 3-manifolds: lens spaces and S1 x S2.
The embedding of two-spheres in the 4-sphere (Bull. AMS) by H. Gluck.
The embedding of two-spheres in the 4-sphere (Trans. AMS) by H. Gluck.
Difféotopies des espaces lenticulaires by F. Bonahon.
On the diffeomorphism group of S1 x S2 by A. Hatcher (original article).
On the diffeomorphism group of S1 x S2 by A. Hatcher (updated version).
Elliptic 3-manifolds: finite fundamental group.
Homotopy of spaces of diffeomorphisms of some 3-dimensional manifolds by N. Ivanov.
Diffeomorphisms of elliptic 3-manifolds by S Hong, J. Kalliongis, D. McCullough, and J.H. Rubinstein.
Homeomorphisms of prism manifolds by K. Asano.
On 3-manifolds that have finite fundamental group and contain Klein bottles by J.H. Rubinstein.
Seifert fibred 3-manifolds.
Seifert fibered spaces by M. G. Brin.
One-sided Heegaard splittings and homeotopy groups of some 3-manifolds by J.H. Rubinstein and J.S. Birman.
Scindements de Heegaard et groupe des homéotopies des petites variétés de Seifert by M. Boileau et Jean-Pierre Otal.
The Smale conjecture for Seifert fibred spaces with hyperbolic base orbifold by D. McCullough and T. Soma.
Haken or sufficiently large 3-manifolds.
On irreducible 3-manifolds which are sufficiently large by F. Waldhausen.
Homeomorphisms of compact 3-manifolds by G.A. Swarup.
On sufficiently large 3-manifolds by G.P. Scott.
Mapping class groups of simple 3-manifolds by K. Johannson.
Virtually geometrically finite mapping class groups of 3-manifolds by D. McCullough.
Recent results on sufficiently large 3-manifolds by F. Waldhausen.
Homeomorphisms of sufficiently large P2 irreducible 3-manifolds by A. Hatcher.
Spaces of incompressible surfaces by A. Hatcher (update of previous article).
Diffeomorphism groups of Waldhausen manifolds by N. Ivanov.
Mostow Rigidity.
Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms by G.D. Mostow.
Strong rigidity of Q-rank 1 lattices by G. Prasad.
The geometry fo finitely generated Kleinian groups by A. Marden.
Mostow's rigidity theorem by J.A. Rodriguez Migueles (Master's thesis).
On Mostow's rigidity theorem by B. Zhang (survey).
Hyperbolic 3-manifolds.
On the geometric and topological rigidity of hyperbolic 3-manifolds by D. Gabai.
Homotopy hyperbolic 3-manifolds are hyperbolic by D. Gabai, G.R. Meyerhoff, and N. Thurston.
The Smale conjecture for hyperbolic 3-manifolds by D. Gabai.
Reducible 3-manifolds.
The homotopy type of homeomorphisms of 3-manifolds by E. César de Sá and C. Rourke (announcement).
Diffeomorphismes des sommes connexes en dimensions trois by H. Hendriks and F. Laudenbach.
On the diffeomorphism group of a redicuble 3-manifold by H. Hendriks and D. McCullough.
Homotopy is not isotopy for homeomorphisms of 3-manifolds by J.L. Friedman and D.M. Witt.
Diffeomorphism groups of reducible 3-manifolds by A. Hatcher (unpublished note).
The mapping class group of connect sums of S2 x S1 by T. Brendle, N. Broaddus, and A. Putman.
Stabilization for mapping class groups of 3-manifolds by A. Hatcher and N. Wahl.
Ricci flow and the generalised Smale conjecture.
Ricci flow and diffeomorphism groups of 3-manifolds by R.H. Bamler and B. Kleiner.
Ricci flow and contractibility of spaces of metrics by R.H. Bamler and B. Kleiner.
Diffeomorphism groups of prime 3-manifolds by R.H. Bamler and B. Kleiner.
Recent developments in Ricci flow by R.H. Bamler.
Classification of diffemorphism groups of 3-manifolds through Ricci flow by R.H. Bamler (slides).