A surface homeomorphism can be thought of as a dynamical system; its mapping torus is a 3-manifold that fibers of a circle; and a Riemannian metric on this 3-manifold determines a path metric on its universal cover. I will discuss how, in some cases, dynamical invariants of the surface homeomorphism, topological invariants of the mapping torus, and geometric invariants of the universal cover are all equivalent. For example, assuming the surface is closed and hyperbolic, then the following are equivalent:

1) the surface homeomorphism has finite order up to isotopy;

2) the mapping torus is finitely covered by a product of the surface and the circle; and

3) the universal cover "is" the product of the hyperbolic plane and the real line.

Zoom Meeting ID: 916 5855 1117

For password see the email or contact: Arunima Ray or Tobias Barthel.

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