Vladimir Turaev develops invariants in low-dimensional topology. His work on Reidemeister torsion refines invariants using Euler structures and relates them to Seiberg-Witten invariant of a three-manifold of three-manifolds.[ref]
A formula for Dehn surgery describes how an invariant changes when a manifold is assembled by filling boundary tori. Tracking the coefficient system and the extra geometric structures is essential: the same underlying filling can have different invariant data. His paper supplies formulas in this refined setting.[ref]
