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Translation distance bounds for fibered 3-manifolds with boundary
by
AJ Stas
CUNY Graduate Center
Given a properly embedded essential surface S with non-zero slope in a fibered hyperbolic 3-manifold M, we show that the translation distance of the monodromy (as it acts on the arc and curve complex of the fiber) can be bounded above by |χ(S)|. We use this result to show that essential surfaces become more complex in covers of M. Furthermore, we show that an infinite family of fibered hyperbolic knots satisfies a conjecture of Schleimer.
Date received: December 23, 2018
Copyright © 2018 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbpq-35.