A Levine–Tristram invariant for knotted tori

Ruberman, Daniel

doi:10.2140/agt.2022.22.2395

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A Levine–Tristram invariant for knotted tori

Daniel Ruberman

Algebraic & Geometric Topology 22 (2022) 2395–2418

DOI: 10.2140/agt.2022.22.2395

Abstract

We define a new topological invariant of an embedded torus in a homology $S^{1} \times S^{3}$ , analogous to the Levine–Tristram invariant of a knot. We compare it to an invariant of smooth tori, defined recently by Echeverria using gauge theory for singular connections.

Keywords

4-manifold, knotted torus, Levine–Tristram invariant

Mathematical Subject Classification

Primary: 57K41, 57K45

References

Publication

Received: 12 October 2020

Revised: 13 March 2021

Accepted: 3 May 2021

Published: 25 October 2022

Authors

Daniel Ruberman
Department of Mathematics Brandeis University Waltham, MA United States

Volume 22, issue 5 (2022)