Algebraic Topology
N J Wildberger
Explore algebraic topology with N J Wildberger's homotopy course! Learn fundamental concepts and build a strong foundation in this fascinating area.
More resources on Homotopy
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab: Homotopy Theory
The nLab entry on homotopy theory, a research-level wiki page surveying the field from a higher-category viewpoint: homotopy categories, model categories, infinity-groupoids, and stable and abstract homotopy theory. It helps readers connect classical topology to modern structural frameworks and references.
Algebraic Topology
Learn homotopy theory with Ryan Budney's Algebraic Topology course! Explore fundamental concepts and build a strong foundation.
Hatcher's Algebraic Topology (free PDF)
Allen Hatcher's standard graduate textbook, freely downloadable from Cornell, covering fundamental groups, homology, cohomology and homotopy theory, with CW complexes introduced in Chapter 0 and used throughout. Readers learn to build spaces from cells and compute their algebraic invariants.
Algebraic Topology II (MIT 18.906)
Detailed lecture notes (about 160 pages) and problem sets on homotopy theory: fibrations and cofibrations, homotopy groups, Whitehead and Hurewicz theorems, obstruction theory, classifying spaces, spectral sequences, characteristic classes and Steenrod operations. Assumes a first graduate course in algebraic topology.
Algebraic Topology
Graduate textbook covering the fundamental group and covering spaces, homology, cohomology with cup products and Poincaré duality, and homotopy theory. Readers learn to compute invariants of spaces and use them to distinguish spaces up to homotopy equivalence.