Algebraic Topology

Livro digital

Título:
Algebraic Topology

Autor:
Allen Hatcher

Categoria:
Matemática & Lógica > Geometria e Topologia

Pessoa doadora:
Raffaello D. N.

Sinopse:
Algebraic Topology opens with Chapter 0’s geometric toolkit, then moves through the fundamental group, covering spaces, homology, and cohomology before returning to homotopy theory in Chapter 4. That structure matters: the book builds the reader from spaces, paths, and cell complexes into the central invariants that let topology become computable. The table of contents shows a wide, carefully ordered progression, from van Kampen’s theorem and ∆complexes to Mayer-Vietoris sequences, cup products, Poincaré duality, Postnikov towers, and obstruction theory. It is a single-author textbook, but it reads with the clarity of a long-refined course, mixing classical foundations with a geometric emphasis that keeps the abstractions anchored in examples. The result is a broad, readable introduction that still reaches deep into the subject’s core techniques. Readers get not just definitions, but a coherent map of how algebraic topology works, where its main tools fit, and why CW complexes, covering spaces, and duality are so central to the field.