Knudson K. Algebraic Topology. A Toolkit 2024

Textbook in PDF format

This book is ideal as an introduction to algebraic topology and applied algebraic topology featuring a streamlined approach including coverage of basic categorical notions, simplicial, cellular, and singular homology, persistent homology, cohomology groups, cup products, Poincare Duality, homotopy theory, and spectral sequences. The focus is on examples and computations, and there are many end of chapter exercises and extensive student projects.
Focuses on (co)homology and its computation with a large collection of examples.
Covers topics such as persistent homology and basic topological data analysis.
Provides many exercises and extended projects to engage students in deeper study.
Preliminaries
Homology
Cohomology and duality
Homotopy and spectral sequences
Bibliography
Index