We prove a local index formula for cusp-pseudodifferential operators on a manifold with boundary. This is known to be equivalent to an index formula for manifolds with cylindrical ends, and hence we obtain a new proof of the classical Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary, as well as an extension of Melrose’s b-index theorem. Our approach is based on ...

In this paper we define and examine the truncated Witten genus. It is defined as the equivariant index of the Dirac operator on the manifold Map(Cp, M) with its natural Cp-action. Here, Map(Cp, M) is the space of maps from the cyclic group of order p into a closed, connected, spin manifold, By applying the Atiyah-Singer index theorem we give a topological formula for the truncated Witten genus ...

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. If the fibers of G → B are simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result being given by an Atiyah-Singer type formula. We also study traces on the corresponding algebras of pseudodifferentia...

This article is devoted to a study of flat orbifold vector bundles. We construct bijection between the isomorphic classes proper bundles and equivalence representations fundamental groups base orbifolds. establish Bismut-Zhang like anomaly formula for Ray-Singer metric on determine line cohomology compact with coefficients in an bundle. show that analytic torsion acyclic unitary bundle equal va...

Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng, Han and He (2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive σ-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which...

We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certa...

We give a derivation of the Verlinde formula for the Gk WZW model from Chern-Simons theory, without taking recourse to CFT, by calculating explicitly the partition function ZΣ×S1 of Σ × S 1 with an arbitrary number of labelled punctures. By a suitable gauge choice, ZΣ×S1 is reduced to the partition function of an Abelian topological field theory on Σ (a deformation of non-Abelian BF and Yang-Mi...

We present the details of our embedding proof, which was announced in [DZ1], of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary [APS1]. Introduction The index theorem of Atiyah, Patodi and Singer [APS1, (4.3)] for Dirac operators on manifolds with boundary has played important roles in various problems in geometry, topology as well as mathematical physics. ...