University of Cambridge > > Differential Geometry and Topology Seminar > Critical points of low index for the systole function

Critical points of low index for the systole function

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  • UserMaxime Fortier-Bourque, Glasgow
  • ClockWednesday 30 January 2019, 16:00-17:00
  • HouseMR13.

If you have a question about this talk, please contact Ivan Smith.

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.

This talk is part of the Differential Geometry and Topology Seminar series.

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