Intersection-number Operators for Curves on Discs Ii

  title={Intersection-number Operators for Curves on Discs Ii},
  author={Stephen P. Humphries},
Let the braid group Bn act as (isotopy classes of) diffeomorphisms of an n-punctured disc Dn. Then there is an action of Bn on a polynomial algebra R = C [a1 , . . . , aN ] and a way of representing simple closed curves on Dn as elements of R. Fix k ∈ 2N. Using this approach we show that the image in Aut(R) of each Dehn twist τ about a simple closed γ in Dn satisfies a kind of characteristic equation when its action is restricted to the image in R of the set of curves γ having geometric… CONTINUE READING