Dehn filling and knot complements that do not irregularly cover

Abstract: It is a longstanding conjecture of Neumann and Reid that exactly three knot complements can irregularly cover a hyperbolic orbifold -- the figure-eight knot and the two Aitchison--Rubinstein dodecahedral knots. This conjecture, when combined with work of Boileau--Boyer--Walsh, implies a more recent conjecture of Reid and Walsh, which states that there are at most three knot complements in the commensurability class of any hyperbolic knot. We give a Dehn filling criterion that is useful for producing large families of knot complements that satisfy both conjectures.

The work we will discuss is partially joint with Hoffman and Millichap and also partially joint with Chesebro, Deblois, Hoffman, Millichap, and Mondal.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( chat | paper | slides )

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Geometry and topology online

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The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.

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