Essential annuli in genus two handlebody exteriors
arxiv(2024)
摘要
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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