Algebraic topology is a twentieth century field of mathematics that can trace its origins and connections back to the ancient beginnings of mathematics. Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology allows for a convenient proof that any subgroup of a free group is again a free group. This book is an introduction to algebraic topology with rather broad coverage of the subject. The book emphasises on homology and cohomology theory, including cup products, Kunneth formulas, intersection pairings, and the Lefschetz fixed point theorem.

Print ISBN: 9781682502983 | $ 170 | 2016 | Hardcover

Contributors: Oliver Knill et al