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Presented By: Department of Mathematics

Student Geometry/Topology

Expanding endomorphisms of compact manifolds

An endomorphism of a Riemannian manifold is said to be expanding if it increases the norm of tangent vectors everywhere (possibly only after a few iterations); the most basic examples of this are the maps $z \mapsto z^n$ for $n > 1$ on the unit circle. We'll show (following Shub) that any two homotopic expanding endomorphisms of a compact manifold are topologically conjugate, and give a correspondence between the conjugating homeomorphisms and (certain) endomorphisms of the fundamental group. I'll assume some basic covering space theory, but not much else. Speaker(s): Salman Siddiqi (UM)

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