RATIONAL HOMOLOGY OF AUT(Fn ) Allen Hatcher * and Karen Vogtmann* ABSTRACT. We compute the rational homology in dimensions less than seven of the group of automorphisms of a finitely generated free group of arbitrary ran

Source URL: www.math.cornell.edu

• Geometric topology
• Algebraic topology
• Homotopy theory
• Fundamental group
• Entailment
• Mapping class group
• Curry–Howard correspondence
• Karen Vogtmann
• Train track map
• Topology
• Mathematics
• Abstract algebra

Stable Homology of Spaces of Graphs Allen Hatcher Stanford July 27, 2012

Source URL: www.math.cornell.edu

• Universal graph
• Line graph
• Graph theory
• Planar graphs
• Graph

A 50 -Year View of Diffeomorphism Groups Allen Hatcher Question: For a smooth compact manifold M can one determine the homotopy type of its diffeomorphism group Diff(M) ? Why this is interesting:

Source URL: www.math.cornell.edu

• Differential topology
• Algebraic topology
• Geometric topology
• Diffeomorphism
• Diff
• Cobordism
• H-cobordism
• Mapping class group
• Characteristic class
• Topology
• Surgery theory
• Abstract algebra

Ian Hatcher b. 1983, Seattle WA [removed] ianhatcher.net

Source URL: ianhatcher.net

homotopy sphere. The Poincar´ e conjecture asserts that S 3 is the only such manifold. (It seems that Poincar´ e himself did not explicitly formulate this as a conjecture.) As we shall see shortly, in the nonsimply-con

Source URL: www.math.cornell.edu

• Haken manifold
• Geometrization conjecture
• Dehn surgery
• Seifert fiber space
• Manifold
• Prime decomposition
• Allen Hatcher
• Orientability
• Topological manifold
• Topology
• 3-manifolds
• Geometric topology

Triangulations of Surfaces Allen Hatcher This is a slightly revised and expanded version of a paper published in 1991 with a very similar title. This paper uses an elementary surgery technique to give a simple topologica

Source URL: www.math.cornell.edu

• Algebraic topology
• Triangulation
• Geometric topology
• Polytopes
• Simplex
• Graph
• Simplicial complex
• Euler characteristic
• Triangle
• Topology
• Mathematics
• Geometry

On the Diffeomorphism Group of S1 × S2 Allen Hatcher This is a revision, written in December 2003, of a paper of the same title that appeared in the Proceedings of the AMS[removed]), [removed].

Source URL: www.math.cornell.edu

• Geometric topology
• Maps of manifolds
• Differential topology
• Algebraic topology
• Homotopy
• Diffeomorphism
• Connected sum
• Isotopy
• CW complex
• Topology
• Abstract algebra
• Homotopy theory

Isoperimetric Inequalities for Automorphism Groups of Free Groups Allen Hatcher * and Karen Vogtmann∗ ABSTRACT. In this paper we show that the groups of automorphisms and outer automorphisms of a finitely generated fre

Source URL: www.math.cornell.edu

• Triangulation
• Geometric topology
• Algebraic topology
• Differential topology
• Simplex
• Isoperimetric inequality
• Simplicial complex
• Mapping class group
• Sphere
• Geometry
• Topology
• Mathematics

CONFIGURATION SPACES OF RINGS AND WICKETS TARA E. BRENDLE AND ALLEN HATCHER Abstract. The main result in this paper is that the space of all smooth links in R3 isotopic to the trivial link of n components has the same ho

Source URL: www.math.cornell.edu

• Maps of manifolds
• General topology
• Link
• Homotopy
• Covering space
• Torus
• Connected space
• Configuration space
• Knot theory
• Topology
• Algebraic topology
• Manifolds

Corrections to the book Algebraic Topology by Allen Hatcher Some of these are more in the nature of clarifications than corrections. Many of the corrections have already been incorporated into later printings of the book

Source URL: www.math.cornell.edu

• Homological algebra
• Homology theory
• Lemmas
• Cohomology
• Čech cohomology
• Closed and exact differential forms
• Function
• Continuous function
• Duality
• Mathematics
• Abstract algebra
• Algebraic topology