Algebraic topology/ Allen Hatcher

By: Hatcher, AllenPublication details: Cambridge: Cambridge University Press, 2002Description: xii, 544 p. : ill. ; 26 cmISBN: 9780521795401; 9780521541862Subject(s): Algebraic topologyDDC classification: 514.2
Contents:
Some Underlying Geometric Notions -- Homotopy and Homotopy Type -- Cell Complexes -- Operations on Spaces -- Two Criteria for Homotopy Equivalence -- The Homotopy Extension Property -- The Fundamental Group -- Basic Constructions -- Paths and Homotopy -- The Fundamental Group of the Circle -- Induced Homomorphisms -- Van Kampen's Theorem -- Free Products of Groups -- The van Kampen Theorem -- Applications to Cell Complexes -- Covering Spaces -- Lifting Properties -- The Classification of Covering Spaces -- Deck Transformations and Group Actions -- Graphs and Free Groups -- K(G,1) Spaces and Graphs of Groups -- Homology -- Simplicial and Singular Homology -- [Delta]-Complexes -- Simplicial Homology -- Singular Homology -- Homotopy Invariance -- Exact Sequences and Excision -- The Equivalence of Simplicial and Singular Homology -- Computations and Applications -- Degree -- Cellular Homology -- Mayer-Vietoris Sequences -- Homology with Coefficients -- The Formal Viewpoint -- Axioms for Homology -- Categories and Functors -- Homology and Fundamental Group -- Classical Applications -- Simplicial Approximation -- Cohomology -- Cohomology Groups -- The Universal Coefficient Theorem -- Cohomology of Spaces -- Cup Product -- The Cohomology Ring -- A Kunneth Formula -- Spaces with Polynomial Cohomology -- Poincare Duality -- Orientations and Homology -- The Duality Theorem -- Connection with Cup Product -- Other Forms of Duality -- Universal Coefficients for Homology -- The General Kunneth Formula.
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Item type Current library Call number Copy number Status Date due Barcode Item holds
General Books General Books Central Library, Sikkim University
General Book Section
514.2 HAT/A (Browse shelf(Opens below)) C1 Available 49792
General Books General Books Central Library, Sikkim University
General Book Section
514.2 HAT/A (Browse shelf(Opens below)) C2 Available 49793
General Books General Books Central Library, Sikkim University
General Book Section
514.2 HAT/A (Browse shelf(Opens below)) C3 Available 49794
General Books General Books Central Library, Sikkim University
General Book Section
514.2 HAT/A (Browse shelf(Opens below)) C4 Available 49795
General Books General Books Central Library, Sikkim University
General Book Section
514.2 HAT/A (Browse shelf(Opens below)) C5 Checked out 25/10/2024 49796
Total holds: 0
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514.2 GRE Algebraic topology a first course/ 514.2 HAT/A Algebraic topology/ 514.2 HAT/A Algebraic topology/ 514.2 HAT/A Algebraic topology/ 514.2 HAT/A Algebraic topology/ 514.2 HAT/A Algebraic topology/ 514.2 HAT/A Algebraic topology/

Some Underlying Geometric Notions --
Homotopy and Homotopy Type --
Cell Complexes --
Operations on Spaces --
Two Criteria for Homotopy Equivalence --
The Homotopy Extension Property --
The Fundamental Group --
Basic Constructions --
Paths and Homotopy --
The Fundamental Group of the Circle --
Induced Homomorphisms --
Van Kampen's Theorem --
Free Products of Groups --
The van Kampen Theorem --
Applications to Cell Complexes --
Covering Spaces --
Lifting Properties --
The Classification of Covering Spaces --
Deck Transformations and Group Actions --
Graphs and Free Groups --
K(G,1) Spaces and Graphs of Groups --
Homology --
Simplicial and Singular Homology --
[Delta]-Complexes --
Simplicial Homology --
Singular Homology --
Homotopy Invariance --
Exact Sequences and Excision --
The Equivalence of Simplicial and Singular Homology --
Computations and Applications --
Degree --
Cellular Homology --
Mayer-Vietoris Sequences --
Homology with Coefficients --
The Formal Viewpoint --
Axioms for Homology --
Categories and Functors --
Homology and Fundamental Group --
Classical Applications --
Simplicial Approximation --
Cohomology --
Cohomology Groups --
The Universal Coefficient Theorem --
Cohomology of Spaces --
Cup Product --
The Cohomology Ring --
A Kunneth Formula --
Spaces with Polynomial Cohomology --
Poincare Duality --
Orientations and Homology --
The Duality Theorem --
Connection with Cup Product --
Other Forms of Duality --
Universal Coefficients for Homology --
The General Kunneth Formula.

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