Isometries of lattices, knot theory and K3 surfaces

Abstract: We give necessary and sufficient conditions for an integral polynomial to be the characteristic polynomial of an isometry of some even, unimodular lattice of given signature. This result has applications in knot theory (existence of knots with given Alexander polynomial and Milnor signatures) as well as to K3 surfaces (existence of K3 surfaces having an automorphism with given dynamical degree).

number theory

Audience: researchers in the discipline

Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11