Morse theory for geodesics in conical manifolds (Q2460796)

In this paper the classical Morse theory for geodesics is extended to the framework of conical manifolds. The main result of the present paper asserts that, although the energy is nonsmooth, we can find a continuous retraction of its sublevels in absence of critical points. In this respect the author provides an appropriate definition of index for isolated critical values and for isolated critical points. It is also shown that Morse relations hold and a definition is given of multiplicity of geodesics which is geometrical meaningful. In the last part of the paper the abstract results are compared with the weak slope approach existing in the literature. Further examples conclude the present paper.