Related papers: Morse Spectra, Homology Measures and Parametric Pa…
We calculate mod-p cohomology of extended powers, and their group completions which are free infinite loop spaces. We consider the cohomology of all extended powers of a space together and identify a Hopf ring structure with divided powers…
We derive universal formulae for integrating out heavy degrees of freedom in scalar field theories up to one-loop level in terms of covariant quantities associated with the geometry of the field manifold. The universal matching results can…
New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds…
Four-dimensional gravity admits many equivalent formulations - metric, Einstein-Cartan, teleparallel, McDowell-Mansouri, among others - each offering distinct advantages, particularly, in view of quantization. We propose a new formulation…
We study the weak convergence (in the high-frequency limit) of the parameter estimators of power spectrum coefficients associated with Gaussian, spherical and isotropic random fields. In particular, we introduce a Whittle-type approximate…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
In 1972, Marcel Berger defined a metric invariant that captures the `size' of k-dimensional homology of a Riemannian manifold. This invariant came to be called the k-dimensional SYSTOLE. He asked if the systoles can be constrained by the…
In the first part, we discuss the interplay between local scale invariance and metric-affine degrees of freedom from few distinct points of view. We argue, rather generally, that the gauging of Weyl symmetry is a natural byproduct of…
The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and…
In physical theories where the energy (action) is localized near a submanifold of Euclidean (Minkowski) space, there is a universal expression for the energy (or the action). We derive a multipole expansion for the energy that has a finite…
Symmetry under a particular class of non-strictly canonical transformation may be used to identify, and subsequently excise degrees of freedom which do not contribute to the closure of the algebra of dynamical observables. Such redundant…
We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.
We prove that if the shape of the metric unit ball in a homogeneous group enjoys a precise symmetry property, then the associated distance yields the standard form of the area formula. The result applies to some classes of smooth and…
Following \cite{citeSavelyevVirtualMorsetheoryon$Omega$Ham$(Momega)$.}, we develop here a connection between Morse theory for the (positive) Hofer length functional $L: \Omega \text {Ham}(M, \omega) \to \mathbb{R}$, with Gromov-Witten/Floer…
We define operator manifolds as manifolds on which a spectral measure on a Hilbert space is given as additional structure. The spectral measure mathematically describes space as a quantum mechanical observable. We show that the vectors of…
We develop tools to study arithmetically induced singular continuous spectrum in the neighborhood of the arithmetic transition in the hyperbolic regime. This leads to first transition-capturing upper bounds on packing and multifractal…
We consider the random point processes on a measure space X defined by the Gibbs measures associated to a given sequence of N-particle Hamiltonians H^{(N)}. Inspired by the method of Messer-Spohn for proving concentration properties for the…
Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner…
By studying spaces of flow graphs in a closed oriented manifold, we construct operations on its cohomology, parametrized by the homology of the moduli spaces of compact Riemann surfaces with boundary marked points. We show that the…
We describe the Goresky-Hingston coproduct on the free loop space with real coefficients via the quasi-isomorphism $C_*(\Lambda M)\simeq C_*(M,C_*(\Omega M))$. This lets us describe the coproduct on the Leray-Serre spectral sequence as the…