Volumes of end-periodic mapping tori
Marissa Loving

TL;DR
This paper provides an overview connecting the dynamics of end-periodic homeomorphisms on infinite-type surfaces to the geometry of their associated mapping tori, extending Brock's finite-type theorem to this setting.
Contribution
It introduces two recent results that relate the dynamics of end-periodic homeomorphisms to the geometry of their mapping tori, generalizing known finite-type theorems.
Findings
Relation between end-periodic homeomorphisms and mapping torus geometry
Extension of Brock's theorem to infinite-type surfaces
Illustrative overview of recent results in the field
Abstract
In this expository paper, we provide an intuition and illustration-driven overview of two recent results that tie the dynamics of certain homeomorphisms of infinite-type surfaces, called end-periodic homeomorphisms, to the geometry of their associated (compactified) mapping tori. These results are analogues of a theorem of Brock in the finite-type setting for mapping tori of pseudo-Anosov homeomorphisms.
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TopicsLiquid Crystal Research Advancements
