Related papers: Transgression of the index gerbe

Consider a spin manifold M, equipped with a line bundle L and an action of a compact Lie group G. We can attach to this data a family Theta(k) of distributions on the dual of the Lie algebra of G. The aim of this paper is to study the…

The purpose of this paper is to develop the theory of holomorphic gerbes on complex tori in a manner analogous to the classical theory for line bundles. In contrast to past studies on this subject, we do not restrict to the case where these…

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 establish the cancellation of the first $2j$ terms in the diagonal asymptotic expansion of the restriction to the $(0,2j)$-forms of the Bergman kernel associated to the spin${}^c$ Dirac operator on high tensor powers of a positive line…

We consider the construction of the basic bundle gerbe on SU(n) introduced by Meinrenken and show that it extends to a range of groups with unitary actions on a Hilbert space including U(n), diagonal tori and the Banach Lie group of unitary…

We study the index bundle of the Dirac-Ramond operator associated with a family $\pi: Z \to X$ of compact spin manifolds. We view this operator as the formal twisted Dirac operator $\dd \otimes \bigotimes_{n=1}^{\infty}S_{q^n}TM_{\C}$ so…

This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the…

This paper develops the notion of implicit Lagrangian systems on Lie algebroids and a Hamilton--Jacobi theory for this type of system. The Lie algebroid framework provides a natural generalization of classical tangent bundle geometry. We…

We introduce the notion of $\epsilon$-irreducibility for arithmetic cycles meaning that the degree of its analytic part is small compared to the degree of its irreducible classical part. We will show that for every $\epsilon>0$ any…

We develop a framework for describing vector bundles on $\mu_n$-gerbes over curves and illustrate the construction through two detailed examples. Using the interpretation of Brauer classes as obstructions to descending determinantal line…

We give a local formula for the index of a transverse Dirac-type operator on a compact manifold with a Riemannian foliation, under the assumption that the Molino sheaf is a sheaf of abelian Lie algebras.

In the theory of so called "Covariant Quantum Mechanics" a basic role is played by Hermitian vector fields on a complex line bundle in the frameworks of Galilei and Einstein spacetimes. In fact, it has been proved that the Lie algebra of…

We study families of Dirac-type operators, with compatible perturbations, associated to wedge metrics on stratified spaces. We define a closed domain and, under an assumption of invertible boundary families, prove that the operators are…

Let $G$ be a compact connected Lie group, and $M$ a compact Hamiltonian $G$-space, with moment map $J$. For each $G$-equivariant Hermitian vector bundle $E$ over $M$, one has an associated twisted Spin-C Dirac operator, whose equivariant…

Suppose that a linear bounded operator $B$ on a Hilbert space exhibits at least linear GMRES convergence, i.e., there exists $M_B<1$ such that the GMRES residuals fulfill $\|r_k\|\leq M_B\|r_{k-1}\|$ for every initial residual $r_0$ and…

We extend the groundbreaking results of Gromov and Lawson on positive scalar curvature and the Dirac operator on complete Riemannian manifolds to Dirac operators defined along the leaves of foliations of non-compact complete Riemannian…

We introduce and study the index morphism for G-invariant leafwise G-transversally elliptic operators on smooth closed foliated manifolds which are endowed with leafwise actions of the compact group G. We prove the usual axioms of excision,…

We prove that isomorphism classes of principal bundles over a diffeological space are in bijection to certain maps on its free loop space, both in a setup with and without connections on the bundles. The maps on the loop space are smooth…

The Dirac operator is considered on a bidimensional domain whose boundary carries the infinite mass boundary condition. The analysis is focused on the existence of discrete spectrum and on its asymptotic description in the thin width limit.…

In the previous paper of the author, motivated by the categorical $p$-adic local Langlands correspondence, the author studied families of $G_K$-equivariant vector bundles over the Fargues-Fontaine curve parametrized by algebraic-affinoid…