From asteroids to bicycles: Degree formulas for higher order linking
(Snacks in TH 935 at 3:30p.m.)
Abstract: The first asteroid, Ceres, was sighted in January of 1801,but was lost shortly afterwards in the sun’s glare. In December of the same year, Gauss awed the scientific community by directing astronomers to Ceres’ precise location in the night sky. His fascination with the motion of the planets, comets and asteroids continued for many decades. In 1833, he wrote down a beautiful integral formula for the “linking number” of a pair of closed obits,which can be interpreted as the degree of a map from the 2-torus to the 2-sphere. In the early 1950’s, John Milnor introduced a family of higher order linking numbers (the “mu-bar invariants”). In this talk I will describe a formula for Milnor’s triple linking number as the”degree” of a map from the 3-torus to the 2-sphere; “bicycles” willcome into play along the way. This is joint work with DeTurck, Gluck, Komendarczyk, Shonkwiler and Vela-Vick.



