Related papers: A Lorentzian Equivariant Index Theorem

In this work we obtain the general form of polynomial mappings that commute with a linear action of a relative symmetry group. The aim is to give results for relative equivariant polynomials that correspond to the results for relative…

The real and imaginary part of any Abelian differential on a compact Riemann surface define two flows on the underlying compact orientable $C^\infty$ surface. Furthermore, these flows induce an interval exchange transformation on every…

In this paper, non-Hamiltonian systems with holonomic constraints are treated by a generalization of Dirac's formalism. Non-Hamiltonian phase space flows can be described by generalized antisymmetric brackets or by general Liouville…

The Dirac's formalism for constrained systems is applied to the analysis of time-dependent Hamiltonians in the extended phase space. We show that the Lewis invariant is a reparametrization invariant and we calculate the Feynman propagator…

We study the Atiyah-Patodi-Singer (APS) index, and its equality to the spectral flow, in an abstract, functional analytic setting. More precisely, we consider a (suitably continuous or differentiable) family of self-adjoint Fredholm…

We prove an integral formula for the spectral flow of differentiable loops of unitaries of the form ${\rm Id}+$Schatten. Our formula is in terms of a regularised winding number, expressed in terms of exact differential forms, and we show…

We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant…

Using the embedded gradient vector field method (see P. Birtea, D. Comanescu, Hessian operators on constraint manifolds, J. Nonlinear Science 25, 2015), we present a general formula for the Laplace-Beltrami operator defined on a constraint…

Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…

A Dirac operator on a complete manifold is Fredholm if it is invertible outside a compact set. Assuming a compact group to act on all relevant structure, and the manifold to have a warped product structure outside such a compact set, we…

In this paper, we introduce several new secondary invariants for Dirac operators on a complete Riemannian manifold with a uniform positive scalar curvature metric outside a compact set and use these secondary invariants to establish a…

We study a noncommutative analogue of a spacetime foliated by spacelike hypersurfaces, in both Riemannian and Lorentzian signatures. First, in the classical commutative case, we show that the canonical Dirac operator on the total spacetime…

We study the Ricci flow for the Lorentzian Einstein-Hilbert action. We show that Einstein gravity emerges as a fixed point of the Einstein-Ricci flow equations and derive a renormalization group flow in Euclidean signature. By considering…

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with…

We study boundary conditions for elliptic operators on non-compact manifolds with boundary via uniform K-homology, a version of K-homology sensitive to the large-scale geometry of the manifold. To that end, we develop the theory of relative…

In this paper, we employ the framework of localization algebras to compute the equivariant K-homology class of the Euler characteristic operator, a central object in studying equivariant index theory on manifolds. This approach provides a…

This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…

We study perturbed Dirac operators of the form $ D_s= D + s\A :\Gamma(E^0)\rightarrow \Gamma(E^1)$ over a compact Riemannian manifold $(X, g)$ with symbol $c$ and special bundle maps $\A : E^0\rightarrow E^1$ for $s>>0$. Under a simple…

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation $(M,\mathcal{F})$ with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on…

Egorov's theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a…