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 so it stays learned.

What you'll learn

18 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 invariants
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 moment just before you'd forget it. A short placement check finds what you already know, so you start Algebraic Topology exactly where it's useful.

Related Abstract & Pure subjects