Invariants of links in (contact) circle bundles
In 1992 Turaev introduced the notions of ``shadows" and ``gleams" to define quantum invariants of links in circle bundles over surfaces. We generalize his shadow link construction to links in circle bundles over orbifolds and then focus on the case where the ambient manifold is equipped with a compatible contact structure. We interpret the gleam of a Legendrian knot in terms of a defining contact form and use it to compute the rational Thurston-Bennequin and rotation numbers. This is joint work with Josh Sabloff.