Bi-invariant metric on groups

Abstract: A bi-invariant metric on a group \(G\) is a metric such that both the right and the left action of \(G\) on itself is by isometries. Examples of such metrics include the Hofer metric on the group of Hamiltonian diffeomorphisms of a symplectic manifold, the reflection length on a Coxeter group, the commutator length and many others mostly in group theory and dynamics. A particularly interesting example is the cancellation length on free groups, which was first discovered by biologists investigating RNA folding.

In the talk, I will discuss various examples, present a sample of results and open problems.

Mathematics

Audience: researchers in the discipline

Selected Topics in Mathematics - Online Edition