The Blanchfield pairing and the twisted Blanchfield pairing are hermitian sesquilinear forms defined on the homology of the exterior of a given knot. These forms contain geometric information about knots, such as the algebraic unknotting number and sliceness. In previous studies on explicit computations of these forms, several methods based on the Wirtinger presentation have been proposed. However, these methods are difficult to apply to knots with large Seifert genera or high crossing numbers, including the torus knots. In this talk, we describe a procedure for computing (twisted) Blanchfield forms using taut identities, and present several computational results for torus knots obtained via this procedure.

学术海报.pdf