Abstract & Pure

Learn Geometric Group Theory

Groups as metric spaces: the word metric, quasi-isometry, growth, hyperbolicity, ends, amenability, and the rigidity theorems that recover algebra from coarse geometry.

Free to start · adaptive placement finds your level · reviews timed so it stays learned.

What you'll learn

18 lessons in Geometric Group Theory

The word metricQuasi-isometryThe Svarc-Milnor lemmaGrowth functionsPolynomial growth and Gromov's theoremIntermediate growthHyperbolic groupsDehn functionsThe word and conjugacy problemsDehn's algorithm and small cancellationEnds of groupsAmenability and Folner sequencesThe boundary at infinityCAT(0) spaces and cube complexesGroups acting on treesOut(F_n) and outer spaceThe Tits alternative and property (T)Lattices and rigidity
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 Geometric Group Theory exactly where it's useful.

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