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##### Topology
Juanita Pinzon-Caicedo, PMA 12.166: Satellite Operations that are not homomorphisms
Monday, February 28, 2022, 02:00pm - 03:00pm
Two knots $K_0$ and $K_1$ are said to be smoothly concordant if the connected sum $K_0\#m(K_1^r)$ bounds a disk smoothly embedded in the 4-ball. Smooth concordance is an equivalence relation, and the set $\mathcal&ob;C&cb;$ of smooth concordance classes of knots is an abelian group with connected sum as the binary operation. Satellite operations, or the process of tying a given knot P along another knot K to produce a third knot P(K), are powerful tools for studying the algebraic structure of the concordance group. In this talk I will describe conditions on the pattern P that suffice to conclude that the function $P:\mathcal&ob;C&cb;\to \mathcal&ob;C&cb;$ is not a homomorphism. This is joint work with Tye Lidman and Allison Miller.
Location: PMA 12.166