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  1. A PDF book by L. Maxim that covers the basics of algebraic topology, including homotopy, homology, cohomology, spectral sequences, fiber bundles, and more. The book contains definitions, examples, exercises, theorems, and applications of various topics in algebraic topology.

  2. This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in spirit, and stays well within the confines of pure algebraic topology. In a sense, the book could have been written thirty or forty years ago since virtually everything in it is at least that old.

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    • 560
  3. A comprehensive and self-contained introduction to algebraic topology, covering homology, cohomology, singular homology, and Čech cohomology. The PDF file contains 34 chapters with proofs, examples, exercises, and references.

    • 1MB
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  4. Note that i∗(n[σp]) = n[σp] 6= 0 for n 6= 0, so i∗ is injective and thus ∂1 = 0. Hence also H1(X) → H1(X, {p}) is an isomorphism. We know that H0(X) = L Z where α runs. through the set of path components of X and i∗ maps onto the factor Z corresponding to the path component of p, hence H0(X) = H0(X, {p}) ⊕ [σp] .

  5. Chapter 1 Introduction Algebraic Topology is the art of turning existence questions in topology into existence questionsinalgebra ...

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  6. These are notes outlining the basics of Algebraic Topology, written for students in the Fall 2017 iteration of Math 101 at Harvard. They cover topics such as topological spaces, continuous maps, homotopy, and the fundamental group.

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  8. archive.org › download › Hatcher_Allen_-_AlgebraicAllen Hatcher - Archive.org

    This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in spirit, and stays well within the confines of pure algebraic topology. In a sense, the book could have been written thirty or forty years ago since virtually everything in it is at least that old.

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