Return to Colloquia & Seminar listing

### Satellite Operations that are not homomorphisms

**Geometry/Topology**

Speaker: | Juanita Pinzon Caicedo, Notre Dame |

Location: | 2112 MSB |

Start time: | Thu, Oct 13 2022, 2:10PM |

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 $\mathcal{C}$ 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 $P:\mathcal{C}\to \mathcal{C}$ is not a homomorphism. This is joint work with Tye Lidman and Allison Miller.