  Co-Euler structures were studied by Burghelea and Haller on closed manifolds
as dual objects to Euler structures. We extend the notion of co-Euler
structures to the situation of compact manifolds with boundary. As an
application, by studying their variation with respect to smooth changes of the
Riemannian metric, co-Euler structures conveniently provide correction terms
that can be taken into account when considering the complex-valued analytic
torsion on bordisms as a Riemannian invariant.
