Browsing by Author "Kim, Heejoung"

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    End-periodic homeomorphisms and volumes of mapping tori
    (Wiley, 2023) Field, Elizabeth; Kim, Heejoung; Leininger, Christopher; Loving, Marissa; Mathematics
    Given an irreducible, end-periodic homeomorphism f:S→S$f: S \rightarrow S$ of a surface with finitely many ends, all accumulated by genus, the mapping torus, Mf$M_f$, is the interior of a compact, irreducible, atoroidal 3-manifold M¯f$øverlineM_f$ with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of M¯f$øverlineM_f$ in terms of the translation length of f$f$ on the pants graph of S$S$. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.
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    Surface Houghton groups
    (Springer Nature, 2024) Aramayona, Javier; Bux, Kai-Uwe; Kim, Heejoung; Leininger, Christopher J.
    For every $$n\ge 2$$, the surface Houghton group $${\mathcal {B}}_n$$is defined as the asymptotically rigid mapping class group of a surface with exactly n ends, all of them non-planar. The groups $${\mathcal {B}}_n$$are analogous to, and in fact contain, the braided Houghton groups. These groups also arise naturally in topology: every monodromy homeomorphism of a fibered component of a depth-1 foliation of closed 3-manifold is conjugate into some $${\mathcal {B}}_n$$. As countable mapping class groups of infinite type surfaces, the groups $$\mathcal {B}_n$$lie somewhere between classical mapping class groups and big mapping class groups. We initiate the study of surface Houghton groups proving, among other things, that $$\mathcal {B}_n$$is of type $$\text {F}_{n-1}$$, but not of type $$\text {FP}_{n}$$, analogous to the braided Houghton groups.