Essential annuli in genus two handlebody exteriors

2024/04/06 by Koda, Yuya, Ozawa, Makoto, Wang, Yi-Sheng · 3 citations
#57K12 (Secondary) #57M50 (Primary) 57M15 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2404.04503

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.

Cited by

• Hyperbolic Brunnian Theta Curves
• Handlebody-knots obtained by tangle replacement
• On symmetry and exterior problems of knotted handlebodies

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