Algebraic Topology: A First Course

by Marvin J. Greenberg, John R. Harper

Overview

Great first book on algebraic topology. Introduces (co)homology through singular theory.

Product Details

ISBN-13:	9780367091880
Publisher:	Taylor & Francis
Publication date:	06/13/2019
Series:	Mathematics Lecture Note Series , #58
Pages:	332
Product dimensions:	6.00(w) x 9.00(h) x (d)

Table of Contents

Preface , Elementary Homotopy Theory , Introduction to Part I , Arrangement of Part I , Homotopy of Paths , Homotopy of Maps , Fundamental Group of the Circle , Covering Spaces , A Lifting Criterion , Loop Spaces and Higher Homotopy Groups , Singular Homology Theory , Introduction to Part II , Affine Preliminaries , Singular Theory , Chain Complexes , Homotopy Invariance of Homology , Relation Between ? 1 and H 1 , Relative Homology , The Exact Homology Sequence , The Excision Theorem , Further Applications to Spheres , Mayer-Vietoris Sequence , The Jordan-Brouwer Separation Theorem , Construction of Spaces: Spherical Complexes , Betti Numbers and Euler Characteristic , Construction of Spaces: Cell Complexes and more Adjunction Spaces , Orientation and Duality on Manifolds , Introduction to Part III , Orientation of Manifolds , Singular Cohomology , Cup and Cap Products , Algebraic Limits , Poincaré Duality , Alexander Duality , Lefschetz Duality , Products and Lefschetz Fixed Point Theorem , Introduction to Part IV , Products , Thom Class and Lefschetz Fixed Point Theorem , Intersection numbers and cup products. , Table of Symbols