Knots, Bands, Integrals, and a little bit of DNA

Vinicio Antonio Gómez Gutiérrez (FC-UNAM)


(Talk in Spanish) In this talk we will talk about a topological invariant, the link number, and its relationship with the Gaussian integral. Then we will talk about two related geometric invariants, one we will call “the total twist of a band” and the other “average Tait number of the knot”. These two geometric invariants are computed by integrals, and we will explore some examples. Also, very briefly, we will consider two ways of modeling a circular DNA molecule, one as a knot, the other as a band, and their relationship to the previous invariants. If time allow us, I will say something about the total curvature of a knot.

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