The goal of the present paper is to calculate the limit of spectrum of the Hodge-de Rham operator under the perturbation of collapse of one part of a connected sum. It takes place in the general problem of blowing up conical singularities introduced in [Maz06] and [Row08]. Le but de ce travail est de calculer la limite du spectre de l’opéateur de Hodgede Rham dans la perturbation obtenue par ef...

Let G be a simply connected compact Lie group. Let Le(G) be the based loop group with the base point e which is the identity element. Let νe be the pinned Brownian motion measure on Le(G) and let α ∈ L(∧T Le(G), νe) ∩ D∞,p(∧1T Le(G), νe) (1 < p < 2) be a closed 1-form on Le(G). Using the results in rough path analysis, we prove that there exists an f ∈ Lloc(Le(G), νe) such that df = α. Moreover...

We propose a generalization of the notion of R-split mixed Hodge structure by defining a Rsplitting level for mixed Hodge structures. This is a discrete invariant taking values in positive integers and equal to 0 for R-split mixed Hodge structures. We describe some properties of this invariant for classical operations on these structures and give some explicit calculation. Résumé Nous proposons...

Context. Globular clusters are representative of the oldest stellar populations. It is thus essential to have a complete census of these systems in dwarf galaxies, from which more massive galaxies are progressively formed in the hierarchical scenario. Aims. We present the results of spectroscopic observations of eight globular cluster candidates in NGC 147, a satellite dwarf elliptical galaxy o...

where ψi = c1(Li) is the first Chern class of Li, and λj = cj(E) is the j-th Chern class of the Hodge bundle. Hodge integrals arise in the calculations of Gromov-Witten invariants by localization techniques [14, 7]. The explicit evaluation of Hodge integrals is a difficult problem. The Hodge integrals involving only ψ classes can be computed recursively by Witten’s conjecture [26] proven by Kon...

Kuga-Satake varieties are abelian varieties associated to certain weight two Hodge structures, for example the second cohomology group of a K3 surface. We start with an introduction to Hodge structures and we give a detailed account of the construction of Kuga-Satake varieties. The Hodge conjecture is discussed in section 2. An excellent survey of the Hodge conjecture for abelian varieties is [...

We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology in the case of twodimensional free U(1) gauge theory. In addition to the usual BRST charge, we deduce a conserved and nilpotent dual-BRST charge under which the gauge-fixing term remains invariant. This charge is the analogue of the adjoint(dual) exterior derivative of differential geometry. The BRST extended Casimir operator, correspon...

We study de Rahm cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S3, the dihedral group D4 and the quaternion group Q. Poincaré duality holds in every case, and under some assumptions (essentially the existence of a top form) we find that it must hold in general. A short review of the bicovariant (noncommutative) differential cal...

For a generic set in the Teichmüller space, we construct a covariant functor with the range in a category of the operator AF -algebras. The functor maps isomorphic Riemann surfaces to the stably isomorphic AF algebras. Our construction is based on a Hodge theory for measured foliations, elaborated by Hubbard, Masur and Thurston. As an application, we consider the following two problems: (i) a c...

Abstract Torsion free connections and a notion of curvature are introduced on the infinite dimensional nonlinear configuration space Γ of a Riemannian manifold M under a Poisson measure. This allows to state identities of Weitzenböck type and energy identities for anticipating stochastic integral operators. The one-dimensional Poisson case itself gives rise to a non-trivial geometry, a de Rham-...