An Introduction to Algebraic Topology by Joseph J. Rotman
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An Introduction to Algebraic Topology

An Introduction to Algebraic Topology


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About the Book

0 Introduction.- Notation.- Brouwer Fixed Point Theorem.- Categories and Functors.- 1.Some Basic Topological Notions.- Homotopy.- Convexity, Contractibility, and Cones.- Paths and Path Connectedness.- 2 Simplexes.- Affine Spaces.- Affine Maps.- 3 The Fundamental Group.- The Fundamental Groupoid.- The Functor ?1.- ?1(S1).- 4 Singular Homology.- Holes and Green's Theorem.- Free Abelian Groups.- The Singular Complex and Homology Functors.- Dimension Axiom and Compact Supports.- The Homotopy Axiom.- The Hurewicz Theorem.- 5 Long Exact Sequences.- The Category Comp.- Exact Homology Sequences.- Reduced Homology.- 6 Excision and Applications.- Excision and Mayer-Vietoris.- Homology of Spheres and Some Applications.- Barycentric Subdivision and the Proof of Excision.- More Applications to Euclidean Space.- 7 Simplicial Complexes.- Definitions.- Simplicial Approximation.- Abstract Simplicial Complexes.- Simplicial Homology.- Comparison with Singular Homology.- Calculations.- Fundamental Groups of Polyhedra.- The Seifert-van Kampen Theorem.- 8 CW Complexes.- Hausdorff Quotient Spaces.- Attaching Cells.- Homology and Attaching Cells.- CW Complexes.- Cellular Homology.- 9 Natural Transformations.- Definitions and Examples.- Eilenberg-Steenrod Axioms.- Chain Equivalences.- Acyclic Models.- Lefschetz Fixed Point Theorem.- Tensor Products.- Universal Coefficients.- Eilenberg-Zilber Theorem and the Künneth Formula.- 10 Covering Spaces.- Basic Properties.- Covering Transformations.- Existence.- Orbit Spaces.- 11 Homotopy Groups.- Function Spaces.- Group Objects and Cogroup Objects.- Loop Space and Suspension.- Homotopy Groups.- Exact Sequences.- Fibrations.- A Glimpse Ahead.- 12 Cohomology.- Differential Forms.- Cohomology Groups.- Universal Coefficients Theorems for Cohomology.- Cohomology Rings.- Computations and Applications.- Notation.


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Product Details
  • ISBN-13: 9780387966786
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Depth: 25
  • Language: English
  • Returnable: N
  • Spine Width: 27 mm
  • Width: 161 mm
  • ISBN-10: 0387966781
  • Publisher Date: 22 Jul 1998
  • Binding: Hardback
  • Height: 243 mm
  • No of Pages: 437
  • Series Title: Graduate Texts in Mathematics
  • Weight: 865 gr


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