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Algebraic Topology by Michael Starbird


MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Algebraic Geometry eBooks . We hope mathematician or person who’s interested in mathematics like these books.


Algebraic Topology written by Michael Starbird This is an other great mathematics book cover the following topics.

  • Introduction
    Basic Examples, Simplices, Simplicial Complexes, 2-manifolds, 2-manifolds as simplicial complexes, 2-manifolds as quotient spaces, Questions

  • 2-manifolds
    Classification of 2-manifolds, Classification Proof I, Classification Proof II, PL Homeomorphism, Invariants, Euler characteristic, Orientability, CW complexes, 2-manifolds with boundary, *Non-compact surfaces

  • Fundamental group and covering spaces
    Fundamental group, Cartesian products, Induced homomorphisms, Retractions and fixed points, Van Kampen’s Theorem I, Van Kampen’s Theorem: simply connected intersection case, Van Kampen’s Theorem: simply connected pieces case, Fundamental groups of surfaces, Van Kampen’s Theorem, II, 3-manifolds, Lens spaces, Knots in S3, Homotopy equivalence of spaces, Higher homotopy groups, Covering spaces, Theorems about groups

  • Homology
    Z2 homology, Simplicial Z2 homology, CW Z2-homology, Homology from parts, special cases, Chain groups and induced homomorphisms, Applications of Z2 homology, Z2 Mayer-Vietoris Theorem, Introduction to simplicial Z-homology, Chains, boundaries, and definition of simplicial Zhomology, Chain groups and induced homomorphisms, Relationship between fundamental group and first homology, Mayer-Vietoris Theorem

  • Review of Point-Set Topology
  • Review of Group Theory
  • Review of Graph Theory
  • The Jordan Curve Theorem

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