Perturbed geodesics on the moduli space of flat connections and Yang-Mills theory

Details Perturbed geodesics on the moduli space of flat connections and Yang-Mills theory Perturbed geodesics on the moduli space of flat connections and Yang-Mills theory

2010-06-28

arxiv.org/abs/1006.5340v1

Matematische Zeitschrift, 2012

Mathematics

Differential Geometry

58 pages, 3 figures

Scientific paper

10.1007/s00209-012-1025-9

If we consider the moduli space of flat connections of a non trivial principal SO(3)-bundle over a surface, then we can define a map from the set of perturbed closed geodesics, below a given energy level, into families of perturbed Yang-Mills connections depending on a small parameter. In this paper we show that this map is a bijection and maps perturbed geodesics into perturbed Yang-Mills connections with the same Morse index.

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