TY - BOOK AU - Hatcher, Allen TI - Algebraic Topology SN - 9780521795401 U1 - 514.2 PY - 2001/// CY - New York PB - Cambridge University Press KW - Algebraic topology KW - Topologia algebraiczna N1 - Chapter 0. Some Underlying Geometric Notions 1 -- Homotopy and Homotopy Type 1 -- Cell Complexes 5 -- Operations on Spaces 8 -- Two Criteria for Homotopy Equivalence 10 -- Homotopy Extension Property 14 -- Chapter 1. Fundamental Group 21 -- 1.1. Basic Constructions 25 -- Paths and Homotopy 25 -- Fundamental Group of the Circle 29 -- Induced Homomorphisms 34 -- 1.2. Van Kampen's Theorem 40 -- Free Products of Groups 41 -- Van Kampen Theorem 43 -- Applications to Cell Complexes 50 -- 1.3. Covering Spaces 56 -- Lifting Properties 60 -- Classification of Covering Spaces 63 -- Deck Transformations and Group Actions 70 -- 1.A. Graphs and Free Groups 83 -- 1.B. K(G,1) Spaces and Graphs of Groups 87 -- Chapter 2. Homology 97 -- 2.1. Simplicial and Singular Homology 102 -- [Delta]-Complexes 102 -- Simplicial Homology 104 -- Singular Homology 108 -- Homotopy Invariance 110 -- Exact Sequences and Excision 113 -- Equivalence of Simplicial and Singular Homology 128 -- 2.2. Computations and Applications 134 -- Degree 134 -- Cellular Homology 137 -- Mayer-Vietoris Sequences 149 -- Homology with Coefficients 153 -- 2.3. Formal Viewpoint 160 -- Axioms for Homology 160 -- Categories and Functors 162 -- 2.A. Homology and Fundamental Group 166 -- 2.B. Classical Applications 169 -- 2.C. Simplicial Approximation 177 -- Chapter 3. Cohomology 185 -- 3.1. Cohomology Groups 190 -- Universal Coefficient Theorem 190 -- Cohomology of Spaces 197 -- 3.2. Cup Product 206 -- Cohomology Ring 211 -- A Kunneth Formula 218 -- Spaces with Polynomial Cohomology 224 -- 3.3. Poincare Duality 230 -- Orientations and Homology 233 -- Duality Theorem 239 -- Connection with Cup Product 249 -- Other Forms of Duality 252 -- 3.A. Universal Coefficients for Homology 261 -- 3.B. General Kunneth Formula 268 -- 3.C. H-Spaces and Hopf Algebras 281 -- 3.D. Cohomology of SO(n) 292 -- 3.E. Bockstein Homomorphisms 303 -- 3.F. Limits and Ext 311 -- 3.G. Transfer Homomorphisms 321 -- 3.H. Local Coefficients 327 -- Chapter 4. Homotopy Theory 337 -- 4.1. Homotopy Groups 339 -- Definitions and Basic Constructions 340 -- Whitehead's Theorem 346 -- Cellular Approximation 348 -- CW Approximation 352 -- 4.2. Elementary Methods of Calculation 360 -- Excision for Homotopy Groups 360 -- Hurewicz Theorem 366 -- Fiber Bundles 375 -- Stable Homotopy Groups 384 -- 4.3. Connections with Cohomology 393 -- Homotopy Construction of Cohomology 393 -- Fibrations 405 -- Postnikov Towers 410 -- Obstruction Theory 415 -- 4.A. Basepoints and Homotopy 421 -- 4.B. Hopf Invariant 427 -- 4.C. Minimal Cell Structures 429 -- 4.D. Cohomology of Fiber Bundles 431 -- 4.E. Brown Representability Theorem 448 -- 4.F. Spectra and Homology Theories 452 -- 4.G. Gluing Constructions 456 -- 4.H. Eckmann-Hilton Duality 460 -- 4.I. Stable Splittings of Spaces 466 -- 4.J. Loopspace of a Suspension 470 -- 4.K. Dold-Thom Theorem 475 -- 4.L. Steenrod Squares and Powers 487 -- Topology of Cell Complexes 519 -- Compact-Open Topology 529 ER -