  Echeverria recently introduced an invariant for a smoothly embedded torus in
a homology $S^1\times S^3$, using gauge theory for singular connections. We
define a new topological invariant of such an embedded torus, analogous to the
classical Levine-Tristram invariant of a knot. In the 3-dimensional situation,
a count of singular connections on a knot complement reproduces the
Levine-Tristram invariant. We compute the invariant for a number of examples
embedded tori, and show that our topological invariant is the same as what one
might expect from Echeverria's invariant. Langte Ma has subsequently shown this
in general.
