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A¹ homotopy theory
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211	HOMOTOPY FORMULA. COHOMOLOGY. Analysis versus topology 1. Homotopy formula. ♥ Definition. The Lie derivative of a differential form ω ∈ Λd (M ) of any Add to Reading List Source URL: www.wisdom.weizmann.ac.il Language: English - Date: 2004-03-30 09:25:46 Homology theory De Rham cohomology Differential form Connection Differential geometry Holomorphic functional calculus Holonomy Mathematical analysis Mathematics Physics
212	More Exercises for Algebraic Topology by Allen Hatcher Chapter[removed]Given a map f : X →Y , show that there exists a map g : Y →X with gf ≃ 11 iff X is a retract of the mapping cylinder Mf[removed]a) Suppose a CW co Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 2013-03-18 16:11:29 Mathematics Homotopy theory CW complex Fundamental group Homotopy group Mayer–Vietoris sequence Homotopy Singular homology Covering space Topology Abstract algebra Algebraic topology
213	CERF THEORY FOR GRAPHS Allen Hatcher and Karen Vogtmann ABSTRACT. We develop a deformation theory for k-parameter families of pointed marked graphs with fixed fundamental group Fn . Applications include a simple geometri Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 1998-12-27 13:43:53 Algebraic topology Geometric topology Fundamental group Homotopy theory Simplex Graph Karen Vogtmann Neighbourhood Triangulation Mathematics Topology Graph theory
214	ERRATUM TO “STABILIZATION FOR THE AUTOMORPHISMS OF FREE GROUPS WITH BOUNDARIES” ALLEN HATCHER AND NATHALIE WAHL The purpose of this note is to point out a gap in an argument in our paper [4] and explain how to fill i Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 2007-09-15 08:10:18 Algebraic topology CW complex Allen Hatcher Torus Isomorphism Topology Mathematics Homotopy theory
215	THE COMPLEX OF FREE FACTORS OF A FREE GROUP Allen Hatcher * and Karen Vogtmann* ABSTRACT. We show that the geometric realization of the partially ordered set of proper free factors in a finitely generated free group of r Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 1998-01-27 12:11:53 Algebraic topology Homotopy theory Topological spaces Geometric topology Building CW complex Triangulation Simplicial complex Simplex Topology Abstract algebra Mathematics
216	Spaces of Incompressible Surfaces Allen Hatcher The homotopy type of the space of PL homeomorphisms of a Haken 3 manifold was computed in [H1], and with the subsequent proof of the Smale conjecture in [H2], the computati Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 1999-06-11 14:52:31 Algebraic topology 3-manifolds Homeomorphisms Haken manifold Diffeomorphism Torus Mapping class group Fiber bundle Homotopy group Topology Homotopy theory Geometric topology
217	Diffeomorphism Groups of Reducible 3-Manifolds Allen Hatcher In a 1979 announcement by C´esar de S´a and Rourke [CR] there is a sketch of an intuitively appealing approach to measuring the difference between the homoto Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 2008-08-12 20:04:07 Differential topology Geometric topology Topological spaces Homotopy group CW complex Homotopy Diffeomorphism Surgery theory Euler characteristic Topology Homotopy theory Algebraic topology
218	A Short Exposition of the Madsen-Weiss Theorem Allen Hatcher The theorem of Madsen and Weiss [MW] identifies the homology of mapping class groups of surfaces, in a stable dimension range, with the homology of a certain i Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 2014-02-12 10:55:42 Geometric topology Homotopy theory Mapping class group Diffeomorphism Orientability Manifold Thom space Homotopy group Homotopy Topology Differential topology Algebraic topology
219	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 Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 1998-12-23 10:36:42 Geometric topology Algebraic topology Homotopy theory Fundamental group Entailment Mapping class group Curry–Howard correspondence Karen Vogtmann Train track map Topology Mathematics Abstract algebra
220	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: Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 2012-05-07 08:19:51 Differential topology Algebraic topology Geometric topology Diffeomorphism Diff Cobordism H-cobordism Mapping class group Characteristic class Topology Surgery theory Abstract algebra

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