Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Short curves of end-periodic mapping tori
Currently, there is a lot of exciting research activity surrounding end-periodic homeomorphisms of infinite-type surfaces. Such homemorphisms admit tame mapping tori, realized as the interior of a compact $3$-manifold with boundary. If the map is additionally assumed to be atoroidal, then with the application of Thurston's hyperbolization program and work of Field--Kim--Leininger--Loving, its mapping torus admits a hyperbolic structure. One may ask: how might topological properties of the map determine geometric data of the hyperbolic manifold?
As an ``infinite type" analogue to work of Minsky in the finite-type setting, we show that given a subsurface $Y\subset S$, the subsurface projections between the ``positive" and ``negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of $Y$ as it resides in $M_f$.
We'll discuss the motivating theory for finite-type surfaces and their associated closed fibered hyperbolic $3$-manifolds, show how these techniques are used in the infinite-type setting and how our main theorems actually give back to the closed, fibered setting.
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