Related papers: $\eta$-invariant and flat vector bundles

We announce a Godbillon-Vey index formula for longitudinal Dirac operators on a foliated bundle $(X,\F)$ with boundary; in particular, we define a Godbillon-Vey eta invariant on the boundary foliation, that is, a secondary invariant for…

We construct eta- and rho-invariants for Dirac operators, on the universal covering of a closed manifold, that are invariant under the projective action associated to a 2-cocycle of the fundamental group. We prove an Atiyah-Patodi-Singer…

We establish a mod 2 index theorem for real vector bundles over 8k+2 dimensional compact pin$^-$ manifolds. The analytic index is the reduced $\eta$ invariant of (twisted) Dirac operators and the topological index is defined through…

In a previous paper, we have defined arithmetic extension groups in the context of Arakelov geometry. In the present one, we introduce an arithmetic analogue of the Atiyah extension that defines an element -- the arithmetic Atiyah class --…

This article deals with two topics: the first, which has a general character, is a variation formula for the the determinant line bundle in non-K\"ahlerian geometry. This formula, which is a consequence of the non-K\"ahlerian version of the…

In "On the calculation of some differential Galois groups" (Invent. Math. 87 (1987), no. 1), Katz defines the notion of a special flat connection on the complex affine line minus the origin, and he shows that the functor which restricts a…

We give a representation of the extension class associated to a holomorphic fibration by curvature, generalizing the work of Atiyah on holomorphic principal bundles in a natural way. As an application, we obtain a nonlinear analogue of the…

Holomorphic gauge fields in N=1 supersymmetric heterotic compactifications can constrain the complex structure moduli of a Calabi-Yau manifold. In this paper, the tools necessary to use holomorphic bundles as a mechanism for moduli…

We introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bundle. As in the classical holomorphic case, this Atiyah…

Associated to each finite dimensional linear representation of a group G, there is a vector bundle over the classifying space BG. This construction was studied extensively for compact groups by Atiyah and Segal. We introduce a homotopy…

Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…

We analyse the homotopy types of gauge groups of principal U(n)-bundles associated to pseudo Real vector bundles in the sense of Atiyah. We provide satisfactory homotopy decompositions of these gauge groups into factors in which the…

For an acyclic representation of the fundamental group of a compact oriented odd-dimensional manifold, which is close enough to a unitary representation, we define a refinement of the Ray-Singer torsion associated to this representation.…

We construct a pair (E ,F), where E is a holomorphic vector bundle over a compact Riemann surface and F a holomorphic subbundle of E, such that both F and E/F admit holomorphic connections, but E does not.

Expressions for the number of moduli of arbitrary SU(n) vector bundles constructed via Fourier-Mukai transforms of spectral data over Calabi- Yau threefolds are derived and presented. This is done within the context of simply connected,…

We show meromorphic extension and analyze the divisors of a Selberg zeta function of odd type $Z_{\Gamma,\Sigma}^{\rm o}(\lambda)$ associated to the spinor bundle $\Sigma$ on odd dimensional convex co-compact hyperbolic manifolds…

We present a derivation-based Atiyah sequence for noncommutative principal bundles. Along the way we treat the problem of deciding when a given $^*$-automorphism on the quantum base space lifts to a $^*$-automorphism on the quantum total…

We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for…

Let $\Gamma$ be a discrete finitely generated group. Let $\hat{M}\to T$ be a $\Gamma$-equivariant fibration, with fibers diffeomorphic to a fixed even dimensional manifold with boundary $Z$. We assume that $\Gamma\to \hat{M}\to…

We define and study a certain category of vector bundles on a p-adic curve to which we can associate in a functorial way finite dimensional p-adic representations of the geometric fundamental group. Among other things we investigate two…