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
Positive scalar curvature and the Dirac operator on complete riemannian manifolds
Properties of a hypothetical exotic complex structure on
We consider almost-complex structures on whose total Chern classes differ from that of the standard (integrable) almost-complex structure. E. Thomas established the existence of many such structures. We show that if there exists an “exotic” integrable almost-complex structures, then the resulting complex manifold would have specific Hodge numbers which do not vanish. We also give a necessary condition for the nondegeneration of the Frölicher spectral sequence at the second level.
Quantum gravity: unification of principles and interactions, and promises of spectral geometry.
Quillen metrics and higher analytic torsion forms.
Real embeddings and eta invariants.
Remarks on flat and differential -theory
In this note we prove some results in flat and differential -theory. The first one is a proof of the compatibility of the differential topological index and the flat topological index by a direct computation. The second one is the explicit isomorphisms between Bunke-Schick differential -theory and Freed-Lott differential -theory.
Rigid versus non-rigid cyclic actions.
Rochlin invariants, theta functions and the holonomy of some determinant line bundles.
Seiberg-Witten Theory
We give an introduction into and exposition of Seiberg-Witten theory.
Semi-free Zp-Actions on Highly-Connected Manifolds.
Smoothing effect for Schrödinger evolution equation via commutator algebra