Essential annuli in genus two handlebody exteriors

Yuya Koda; Makoto Ozawa; Yi-Sheng Wang

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arXiv · 2404.04503

Essential annuli in genus two handlebody exteriors

Yuya Koda·Makoto Ozawa·Yi-Sheng Wang

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Abstract

We classify all potential configurations of essential annuli in a genus two atoroidal handlebody exterior in the $3$-sphere, building on two recent classifications: the classification of the JSJ-graph of the exterior and the classification of essential annuli in the exterior. In contrast to knots, genus two handlebody exteriors may contain infinitely many non-isotopic essential annuli, due to the JSJ-graph classification. Our main result characterizes the numbers of different types of essential annuli in such an infinite family.

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Yuya Koda, Makoto Ozawa, Yi-Sheng Wang. 2024-04-06. Essential annuli in genus two handlebody exteriors. https://arxiv.org/abs/2404.04503

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