On Chern-Simons invariants of geometric 3-manifolds.
On gluing formulas for the spectral invariants of Dirac type operators.
On the Burns-Epstein invariants of spherical CR 3-manifolds
In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.
On the eta invariant, stable positive scalar curvature, and Higher -genera.
On the index of spin Dirac operators on conical manifolds
We compute the index of the Dirac operator on a spin Riemannian manifold with conical singularities, acting from to with p,q > 1. When 1 + n/p - n/q > 0 we obtain the usual Atiyah-Patodi-Singer formula, but with a spectral cut at (n+1)/2 - n/q instead of 0 in the definition of the eta invariant. In particular we reprove Chou’s formula for the L² index. For 1 + n/p - n/q ≤ 0 the index formula contains an extra term related to the Calderón projector.
On the rho invariant for manifolds with boundary.