Essential annuli in genus two handlebody exteriors
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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