  We introduce new topological quantum invariants of compact oriented
3-manifolds with boundary where the boundary is a disjoint union of two
identical surfaces. The invariants are constructed via surgery on manifolds of
the form $F \times I$ where $I$ denotes the unit interval. Since virtual knots
and links are represented as links in such thickened surfaces, we are able also
to construct invariants in terms of virtual link diagrams (planar diagrams with
virtual crossings).
  These invariants are the first meaningful, nontrivial, and calculable
examples of quantum invariants of 3-manifolds with non-vacuous boundary.
  We give a new invariant of classical links in the 3-sphere in the following
sense: Consider a link $L$ in $S^3$ of two components. The complement of a
tubular neighborhood of $L$ is a manifold whose boundary consists in two copies
of a torus. Our invariants apply to this case of bounded manifold and give new
invariants of the given link of two components. Invariants of knots are also
obtained.
