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A Levine–Tristram invariant for knotted tori

### Daniel Ruberman

Algebraic & Geometric Topology 22 (2022) 2395–2418
##### Abstract

We define a new topological invariant of an embedded torus in a homology ${S}^{1}×{S}^{3}$, 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
##### Publication
Revised: 13 March 2021
Accepted: 3 May 2021
Published: 25 October 2022
##### Authors
 Daniel Ruberman Department of Mathematics Brandeis University Waltham, MA United States