On Bojarski's index formula for nonsmooth interfaces.
On Invariants of Hirzebruch and Cheeger-Gromov.
On some analytical index formulas related to operator-valued symbols.
On the fixed point formula for Atiyah and Bott
On the Heat Equation and the Index Theorem.
On the Index of Callias-type Operators.
On the index of nonlocal elliptic operators for compact Lie groups
We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.
On the index theorem for symplectic orbifolds
We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula.
On the intersection forms of spin 4-manifolds bounded by spherical 3-manifolds.
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.
Opérateurs transversalement elliptiques et formes différentielles équivariantes