From asteroids to bicycles

4:00 pm Thursday, December 3, 2009
Paul Melvin (Bryn Mawr College/ MSRI)


The linking number of a pair of closed curves in 3-space can be expressed as the degree of a map from the 2-torus to the 2-sphere, by means of the linking integral Gauss wrote down in 1833. 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; asteroids and bicycles will come into play along the way. This is joint work with DeTurck, Gluck, Komendarczyk, Shonkwiler and Vela-Vick.

 

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