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About this product
- Author(s)Anant R. Shastri
- PublisherTaylor & Francis Inc
- Date of Publication23/10/2013
- GenreScience & Mathematics: Textbooks & Study Guides
- Place of PublicationBosa Roca
- Country of PublicationUnited States
- ImprintCRC Press Inc
- Content Note59 black & white illustrations, 2 black & white tables
- Weight1179 g
- Width178 mm
- Height254 mm
- Format DetailsUnsewn / adhesive bound
- Table Of ContentsIntroduction The Basic Problem Fundamental Group Function Spaces and Quotient Spaces Relative Homotopy Some Typical Constructions Cofibrations Fibrations Categories and Functors Cell Complexes and Simplicial Complexes Basics of Convex Polytopes Cell Complexes Product of Cell Complexes Homotopical Aspects Cellular Maps Abstract Simplicial Complexes Geometric Realization of Simplicial Complexes Barycentric Subdivision Simplicial Approximation Links and Stars Covering Spaces and Fundamental Group Basic Definitions Lifting Properties Relation with the Fundamental Group Classification of Covering Projections Group Action Pushouts and Free Products Seifert-van Kampen Theorem Applications Homology Groups Basic Homological Algebra Singular Homology Groups Construction of Some Other Homology Groups Some Applications of Homology Relation between pi1 and H1 All Postponed Proofs Topology of Manifolds Set Topological Aspects Triangulation of Manifolds Classification of Surfaces Basics of Vector Bundles Universal Coefficient Theorem for Homology Method of Acyclic Models Homology with Coefficients: The Tor Functor Kunneth Formula Cohomology Cochain Complexes Universal Coefficient Theorem for Cohomology Products in Cohomology Some Computations Cohomology Operations; Steenrod Squares Homology of Manifolds Orientability Duality Theorems Some Applications de Rham Cohomology Cohomology of Sheaves Sheaves Injective Sheaves and Resolutions Cohomology of Sheaves Cech Cohomology Homotopy Theory H-Spaces and H0-Spaces Higher Homotopy Groups Change of Base Point The Hurewicz Isomorphism Obstruction Theory Homotopy Extension and Classification Eilenberg-Mac Lane Spaces Moore-Postnikov Decomposition Computation with Lie Groups and Their Quotients Homology with Local Coefficients Homology of Fibre Spaces Generalities about Fibrations Thom Isomorphism Theorem Fibrations over Suspensions Cohomology of Classical Groups Characteristic Classes Orientation and Euler Class Construction of Steifel-Whitney Classes and Chern Classes Fundamental Properties Splitting Principle and Uniqueness Complex Bundles and Pontrjagin Classes Spectral Sequences Warm-Up Exact Couples Algebra of Spectral Sequences Leray-Serre Spectral Sequence Some Immediate Applications Transgression Cohomology Spectral Sequences Serre Classes Homotopy Groups of Spheres Hints and Solutions Bibliography Index Exercises appear at the end of each chapter.
- Author BiographyDr. Anant R. Shastri is a professor in the Department of Mathematics at the Indian Institute of Technology Bombay, where he has been teaching for over 20 years. His research focuses on the topology of matrix varieties.
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