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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**.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.- 7MB

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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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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] .

Chapter 1 Introduction

**Algebraic Topology**is the art of turning existence questions in**topology**into existence questionsinalgebra ...- 1MB

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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.People also ask

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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.