Related papers: Double transgressions and Bott-Chern duality
We generalize a theorem of Bismut-Zhang, which extends the Cheeger-Mueller theorem on Ray-Singer torsion and Reidemeister torsion, to the case where the flat vector bundle over a closed manifold carries a nondegenerate symmetric bilinear…
In this article, we present two structural results about the Renaudineau-Shaw spectral sequence that computes the cohomology of T-hypersurfaces. The first is a Poincar{\'e} duality satisfied by all its pages of positive index. The second is…
We construct, out of modular symbols, 1-traces that are invariant with respect to the actions of the Hopf algebra $\Hc_{1}$ on the crossed product $\Ac_{Q}$ of the algebra of modular forms of all levels by $\GL^+ (2,Q)$ investigated in…
We observe that linear relations among Chern-Mather classes of projective varieties are preserved by projective duality. We deduce the existence of an explicit involution on a part of the Chow group of projective space, encoding the effect…
Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in…
We exploit the standard tools and techniques of the augmented version of Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry transformations for the…
In this work we apply different duality techniques, both the dual projection, based on the soldering formalism and the master action, in order to obtain and study the dual description of the Carroll-Field-Jackiw model \cite{cfj}, a theory…
We study dg-manifolds which are R[2]-bundles over R[1]-bundles over manifolds, we calculate its symmetries, its derived symmetries and we introduce the concept of T-dual dg-manifolds. Within this framework we construct the T-duality map as…
The self-duality of chiral p-forms was originally investigated by Pasti, Sorokin and Tonin in a manifestly Lorentz covariant action with non-polynomial auxiliary fields. The investigation was then extended to other chiral p-form actions. In…
A theory of differential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a…
The self-dual double copy is further explored. In previous work, it has been shown that hyper-Hermitian manifolds also have associated the self-dual gauge theories via Kerr-Schild double copy. The self-dual double copy is generalized in the…
Chiral bosons, or self-dual p-form fields, are ubiquitous in string theoretic contexts but are challenging to treat. Lagrangian constructions invariably introduce a complexity be it auxiliary fields or sacrificing Lorentz invariance. In…
Within the superfield approach, we consider the duality between the supersymmetric Maxwell-Chern-Simons and self-dual theories in three spacetime dimensions. Using a gauge embedding method, we construct the dual theory to the self-dual…
We present superstring Lagrangians with manifest T-duality. The Lagrangian version of the section conditions are necessary to make Lagrangians to be general coordinate invariant. We show the general solution of section conditions. The…
The goal of the paper is two-fold. At first, we attempt to give a survey of some recent applications of symmetric polynomials and divided differences to intersection theory. We discuss: polynomials universally supported on degeneracy loci;…
For having a Poincar\'e duality via a cap product between the intersection homology of a paracompact oriented pseudomanifold and the cohomology given by the dual complex, G. Friedman and J. E. McClure need a coefficient field or an…
We propose a generalization of the Hodge $dd_c$-lemma to the case of hyperk\"ahler manifolds. As an application of this result we derive the global construction of the fourth order transgression of the Chern character forms of…
This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps $\alpha : E \rightarrow F$ which, for smooth…
We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on…
The aim of these notes, originally intended as an appendix to a book on the foundations of equivariant cohomology, is to set up the formalism of the $G$-equivariant Poincar\'e duality for oriented $G$-manifolds, for any connected compact…