Low index singularities of the systole function - Note Thursday!
Analysis and Geometry Seminar
29th November 2018, 3:00 pm – 4:00 pm
Howard House, 4th Floor Seminar Room
The systole of a hyperbolic surface is the length of any of its shortest geodesics. Akrout showed that this defines a topological Morse function on the Teichmuller space of the surface. As such, the critical points of the systole function carry information about the topology of moduli space. Schmutz Schaller found a critical point of index 2g-1 in every genus g>1 and conjectured that this was the smallest index possible, because of the virtual cohomological dimension of moduli space calculated by Harer. I will describe a family of counterexamples: for every c>0, there exists a closed hyperbolic surface of genus g which is a critical point of index at most cg.