A talk at Banff in December 2012 about an analog of the Madsen-Weiss theorem for certain 3-manifolds.
"Assembling homology classes in automorphism groups of free groups" (with Jim Conant, Martin Kassabov, and Karen Vogtmann).
This version posted February 2014.
This is a 12-page excerpt from a joint paper with Pierre Lochak and Leila Schneps On the Teichmuller Tower of Mapping Class Groups.Pdf file (43 pages).The main reason for this is that the book is used as a textbook at a number of universities where the problem sets count for part of a student's grade.Pdf file "Pants decompositions of surfaces" pdf file.Slides of Talks: Stable homology of spaces of graphs.This is also unfinished, but the aim is to mio map product key describe the homotopy types of the components of the space of all knots in the 3-sphere.Note: Section.2 has been revised from the original version, necessitating a renumbering of items.11-3.21.Book Projects, algebraic Topology, this book, published in 2002, is a beginning graduate-level textbook on algebraic topology from a fairly classical point of view.Pdf file (7 pages).Papers published since 1996: "Tethers and homology stability for surfaces" (with Karen Vogtmann)."Stabilization for the automorphisms of free groups with boundaries" (with Nathalie Wahl).I have now returned to an earlier plan of having this material be an extra chapter of the Algebraic Topology book, rather than a separate book.Vector Bundles and K-Theory, this unfinished book is intended to be a fairly short introduction to topological K-theory, starting with the necessary background material on vector bundles and including also basic material on characteristic classes.Here are some Pictures of Bianchi orbifolds.Topology of Numbers, this is intended to be an undergraduate textbook presenting a somewhat geometrically-flavored introduction to elementary number theory.Geometry and Topology 9 (2005.
This is an expository account of the classical theorems that topological surfaces have unique smooth structures, and homeomorphisms of smooth surfaces are isotopic to diffeomorphisms.
A talk at Luminy in June 2010 outlining the current simplified form of the proof of Galatius' theorem on the stable homology of Aut(F_n with comments on how the Madsen-Weiss theorem follows similarly, as do a couple analogs in dimension three involving handlebodies.