Infinite volume and infinite injectivity radius

Abstract: We prove the following conjecture of Margulis. Let G be a higher rank simple Lie group and Λ a discrete subgroup. Then vol(G/Λ) is finite if and only if there is a compact set in G which intersects nontrivially every conjugate of Λ. In the special case where Λ is a normal subgroup of a lattice this is the celebrated normal subgroup theorem of Margulis. [This is joint work with Mikolaj Fraczyk.]

algebraic geometrydifferential geometrygroup theorygeometric topologynumber theory

Audience: general audience

International Conference on Discrete groups, Geometry and Arithmetic

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