Nattalie Tamam Imperial College

Markoff triples and their connection to orbits of the mapping class group

Abstract:

The Markoff triples are the natural solutions of the Markoff relation x²+y²+z²=3xyz. They can be viewed as points in the orbit of the mapping class group acting on the character variety of the punctured torus. In this case the action is transitive. However, when considering surfaces with a higher genus or number of holes, this is no longer the case. We will discuss the possible orbits closures of the general case; the algebraic relations that are preserved under the action and the exceptional cases. This is a joint work with Alireza Salehi-Golsefidy.