Non-characterising slopes for satellite knots

Laura Wakelin (Max Planck Institute for Mathematics)

Monday 26th February 16:00-17:00 Maths 311B

Abstract

A slope p/q is non-characterising for a knot K in the 3-sphere if there exists a different knot K’ in the 3-sphere such that Dehn surgery of slope p/q on each of K and K’ produces orientation-preserving homeomorphic 3-manifolds. In this talk, we will explore 3 different approaches to constructing non-characterising slopes for satellite knots. For the |p|=1 case, I’ll describe how to use JSJ decompositions to find suitable satellite knots of hyperbolic type (joint work with Patricia Sorya). For the |q|=1 case, I’ll discuss how to use RBG links to address certain knots concordant to satellites of (2,k)-torus knots (joint work with Charles Stine). Finally, for the general p/q case, I’ll explain how the Montesinos trick could potentially be used to show that every p/q can be realised as a non-characterising slope for some pair of satellite knots (joint work with Kyle Hayden and Lisa Piccirillo). 

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