# The injectivity radius of hyperbolic surfaces and some Morse functions over moduli spaces

@article{Gendulphe2015TheIR, title={The injectivity radius of hyperbolic surfaces and some Morse functions over moduli spaces}, author={Matthieu Gendulphe}, journal={arXiv: Geometric Topology}, year={2015} }

This article is devoted to the variational study of two functions defined over some Teichmueller spaces of hyperbolic surfaces. One is the systole of geodesic loops based at some fixed point, and the other one is the systole of arcs.\par For each of them we determine all the critical points. It appears that the systole of arcs is a topological Morse function, whereas the systole of geodesic loops have some degenerate critical points. However, these degenerate critical points are in some sense…

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