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HYPERBOLIC SECTIONS IN SEIFERT-FIBERED SURFACE BUNDLES image

HYPERBOLIC SECTIONS IN SEIFERT-FIBERED SURFACE BUNDLES


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•November 9, 2009
5:30 pm 

HYPERBOLIC SECTIONS IN SEIFERT-FIBERED SURFACE BUNDLES art
 


Let M be a small Seifert fiber space which has also a structure of surface bundle F x [0, 1]/{(x, 0) = (f(x), 1)} over the circle, where f: F -> F is a monodromy map with non-empty fixed point set. A typical example of such a manifold appears as the result of 0-surgery on a torus knot. For each section in M, we have a ‘projection’ in F in a natural way. We give a condition assuring that the given section in M is hyperbolic in terms of the ‘projection’ in the fiber surface. By translating the result, we give a condition to obtain pseudo-Anosov automorphisms of once punctured surfaces from a periodic automorphism.

Source:HYPERBOLIC SECTIONS IN SEIFERT-FIBERED SURFACE BUNDLES


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