Course Archives Theoretical Statistics and Mathematics Unit

Course: Geometric Group Theory Level: Undergraduate Time: Currently not offered

Syllabus Past Exams Syllabus: Review of group theory (basic notions and operations with groups, solvable and nilpotent groups), Groups with generators and relations: Generating sets,free groups, reduced words, presentation of a group, finitely presented groups.Products and extensions of groups, free products and amalgamated free products. Groups and their Cayley graphs, trees and free groups, Review of groups actions, free actions, orbits and stabilisers, transitive actions. Free groups and actions on trees, The ping-pong lemma, The Tits alternative. Quasi-isometry of metric spaces, quasi-isometry type of groups, quasi-geodesic and quasi-geodesic spaces, the ˇSvarc-Milnor Lemma with applications, quasi-isometry invariants. Growth of groups, growth types, groups of polynomial growth, groups of uniform exponential growth. ADDITIONAL TOPICS FROM: Hyperbolic groups, Ends and boundaries, Amenable groups. Reference Texts: (a) Clara Loh: Geometric Group Theory: An introduction. (b) Pierre de la Harpe: Topics in Geometric Group Theory. (c) John Meier: Groups, Graphs and Trees: An introduction to the geometry of infinite groups. (d) M. Clay and D. Margalit: Office Hours with a geometric group theorist. Top of the page Past Exams

Midterm 25.pdf Semestral 25.pdf Supplementary and Back Paper 25.pdf Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]