A link invariant with values in the Witt ring

TL;DR

This paper introduces a new link invariant valued in Witt rings, connecting classical invariants and the Weil representation through Maslov indices, expanding the algebraic tools for link classification.

Contribution

It presents a novel link invariant in Witt rings derived from Maslov indices, linking classical invariants and the Weil representation.

Findings

Existence of oriented link invariants in Witt rings

Connection between classical invariants and the new construction

Relation to the Weil representation

Abstract

Using Maslov indices, we show the existence of oriented link invariants with values in the Witt rings of certain fields. Various classical invariants are closely related to this construction. We also explore a surprising connection with the Weil representation. This version is identical to the one accepted for publication in Quantum Topology.