Great first book on algebraic topology. Introduces (co)homology through singular theory.
By:
Marvin J. Greenberg,
John R. Harper
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions:
Height: 229mm,
Width: 152mm,
Weight: 771g
ISBN: 9780367091880
ISBN 10: 0367091887
Pages: 332
Publication Date: 13 June 2019
Audience:
College/higher education
,
General/trade
,
Primary
,
ELT Advanced
Format: Hardback
Publisher's Status: Active
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
