Abstract & Pure

Learn Algebraic Topology

Computing the invariants that `topology` names: homology by hand from a triangulation, covering spaces as a Galois correspondence, and the stable theory above the first course.

Free to start · adaptive placement finds your level · reviews timed to your own forgetting.

What you'll learn

30 lessons in Algebraic Topology

Computing homology by handThe nerve theoremDiscrete Morse theoryCovering spaces as a Galois correspondenceNielsen-Schreier by covering spacesEilenberg-MacLane spacesPostnikov towersClassifying spacesThe Serre spectral sequenceSteenrod squaresFreudenthal suspension and stabilisationSpectraPontryagin-Thom and cobordismK-theory and Bott periodicityHopf invariant oneThe Lefschetz fixed point formulaAlexander dualityReading a space off its invariantsCellular approximationCW approximation and the Whitehead theoremThe homotopy fibre and the Puppe sequenceHomotopy pushoutsHomotopy limitsObstruction theoryThe Bockstein homomorphismThe Steenrod algebra and admissible monomialsThe Adams spectral sequenceSerre finitenessRational homotopy and minimal modelsLocalisation and the arithmetic square
How Erudia teaches

Built to be understood — and remembered.

Every idea is taught with motivation and a worked example before the drills, and an FSRS spaced-repetition engine schedules each review for the day its model predicts you would forget it. A short placement check finds what you already know, so you start Algebraic Topology exactly where it's useful.

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