Master thesis presentation by Juan Felipe Celis Rojas
Title: Homology of Sullivan diagrams
Speaker: Juan Felipe Celis Rojas
Abstract: We study the homology of the harmonic compactification of the moduli space of Riemann surfaces. This compactification admits a model with metric fat graphs called Sullivan diagrams. First, we do some new computations of fundamental groups for spaces of Sullivan diagrams. Then we give a new proof of homological stability for Sullivan diagrams with respect to punctures and boundary components. This proof includes a computation of the stable homology of Sullivan diagrams. Finally, we fit stabilisation with respect to genus in the homological stability machinery and we state a conjecture on the stability range.