Amenability and Growth of Closed Geodesics for Regular Covers

Rhiannon Dougall (University of Warwick)

Frank Adams 1, Alan Turing Building,

For compact (or convex co-compact) negatively curved Riemannian man-
ifolds, a classical object of study is the exponential growth rate of closed
geodesics, which is equal to the topological entropy of the geodesic ow. In
this talk, we discuss the corresponding growth rate of closed geodesics for reg-
ular covering manifolds of compact (or convex co-compact) manifolds. Since
the growth rate for the cover is always smaller than (or equal to) the growth
rate for the base manifold, we ask when we have equality. The answer to this
depends only on an abstract property of the covering group. This is joint
work with Richard Sharp.

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