Related papers: Induced differential characters on nonlinear Gra{\…
The slightly subtle notion of covariant Lie derivatives of \textit{bundle-valued} differential forms is crucial in many applications in physics, notably in the computation of conserved currents in gauge theories, and yet the literature on…
Given a double cover $\pi: \mathcal{G} \rightarrow \hat{\mathcal{G}}$ of finite groupoids, we explicitly construct twisted loop transgression maps, $\tau_{\pi}$ and $\tau_{\pi}^{ref}$, thereby associating to a Jandl $n$-gerbe…
We consider irreducible representations of finite quandles over $\mathbb{C}$. For $Q$ a finite quandle whose inner automorphism group $Inn(Q)$ have trivial Schur multipliers, we prove that the irreducible representations of $Q$ can be…
The intuitive notion of the Gromov invariant for maps from a Riemann surface to a Grassmannian is shown to agree with the definition in \cite{BDW}. Also, an induction on the genus is proved, which extends the results of \cite{BDW} to a…
In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem;…
For a manifold $M$ with an integral closed 3-form $\omega$, we construct a $PU(H)$-bundle and a Lie groupoid over its total space, together with a curving in the sense of gerbes. If the form is non-degenerate, we furthermore give a natural…
This paper defines an asymptotic character map which is a morphism from the Grothendieck group of category $\mathcal{O}$ of an integral filtered quantization to rational functions on the Lie algebra of a torus. We show that the asymptotic…
The paper is another step towards a realisation of the goal, advanced in articles 1706.05682 [hep-th] and 1808.04470 [hep-th], of a systematic supersymmetry-equivariant geometrisation of physically distinguished Green-Schwarz…
Given a connection on a meromorphic vector bundle over a compact Riemann surface with reductive Galois group, we associate to it a projective variety. Connections such that their associated projective variety are curves can be classified,…
In this paper we use character variety methods to study homomorphisms between the fundamental groups of 3-manifolds, in particular those induced by non-zero degree maps. A {\it knot manifold} is a compact, connected, irreducible, orientable…
It is shown that vielbeins and connections of any (super)space are naturally described in terms of nonlinear realizations of infinite - dimensional diffeomorphism groups of the corresponding (super)space. The method of construction of…
We give a geometric perspective on the algebra of Drinfeld modular forms for congruence subgroups $\Gamma\leq \GL_2(\bbF_q[T]).$ In particular, we describe an isomorphism between the section ring of a line bundle on the stacky modular curve…
This work gives a version of the Eichler-Shimura isomorphism with a non-abelian $H^1$ in group cohomology. Manin has given a map from vectors of cusp forms to a noncommutative cohomology set by means of iterated integrals. We show Manin's…
Let (M,g) be a compact Riemannian manifold of dimension n. For k \in {0,...,n}, we denote Gr_{k}(M) the set of compact, connected and oriented submanifolds of M of dimension k. This set is called the non-linear Grassmannian. In this…
This paper investigates the transfer of classical geometric structures from a smooth manifold $M$ to its Weil bundle $(M^\mathbf A, \tilde\pi_M, M)$ associated with a Weil algebra $\mathbf A$. We show that various structures including…
We show that the space of all holomorphic maps of degree one from the Riemann sphere into a Grassmann manifold is a sphere bundle over a flag manifold. Using the notions of "kernel" and "span" of a map, we completely identify the space of…
Let $A$ be a ring equipped with a derivation $\delta $. We study differential Azumaya $A$ algebras, that is, Azumaya $A$ algebras equipped with a derivation that extends $\delta $. We calculate the differential automorphism group of the…
We prove a `Whitney' presentation, and a `Coulomb branch' presentation, for the torus equivariant quantum K theory of the Grassmann manifold $\mathrm{Gr}(k;n)$, inspired from physics, and stated in an earlier paper. The first presentation…
We introduce a new spectral sequence for the study of $\mathcal{K}$-manifolds which arises by restricting the spectral sequence of a Riemannian foliation to forms invariant under the flows of $\{\xi_1,...,\xi_s\}$. We use this sequence to…
We show that there is an infinite group of special automorphisms of the deformed group of diffeomorphisms, which describes parallel transports in Riemannian spaces of any variable curvature. Generators of translations of such group contain…