Related papers: Free loop spaces and the Cauchy--Frobenius Lemma

We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual: namely, starting from a quantum coisotropic subgroup (for a quantization of a given Poisson group) we provide functorial recipes to…

Recently R. Cohen and V. Godin have proved that the homology of the free loop space of a closed oriented manifold with coefficients in a field has the structure of a Frobenius algebra without counit. In this short note we prove that when…

We prove that Bourgain's separation lemma, Lemma~20.14 [B2] holds at fixed frequencies and their neighborhoods, on sub-lattices, sub-modules of the dual lattice associated with a quasi-periodic Fourier series in two dimensions. And by…

We continue our investigation of an improved quantization scheme for spherically symmetric loop quantum gravity. We find that in the region where the black hole singularity appears in the classical theory, the quantum theory contains…

This paper develops a novel approach to functorial quantum field theories (FQFTs) in the context of Lorentzian geometry. The key challenge is that globally hyperbolic Lorentzian bordisms between two Cauchy surfaces cannot change the…

This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both…

We give an explicit way of calculating the set of homotopy classes of morphisms from a Tamsamani n-category A to another one B. This calculation uses a Reedy-cofibrant cosimplicial resolution of A, using a new notion of ``free cofibration''…

The philosophy of the Loop Quantum Gravity approach is to construct the canonical variables by using the duality of infinitesimal connections and holonomies along loops. Based on this fundamental property for example the holonomy-flux…

We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter $\gamma$. This construction deeply relies on the link between black holes and…

We study Verdier quotients of diverse homotopy categories of a full additive subcategory $\mathcal E$ of an abelian category. In particular, we consider the categories $K^{x,y}({\mathcal E})$ for $x\in\{\infty, +,-,b\}$, and…

We give a new, unexpected characterization of saturated fusion systems on a p-group S in terms of idempotents in the p-local double Burnside ring of S that satisfy a Frobenius reciprocity relation, and reformulate fusion-theoretic phenomena…

Homotopy Quantum Field Theories as variants of Topological Quantum Field Theories are described by functors from some cobordism category, enriched with homotopical data, to a symmetric monoidal category $\mathcal{V}$. A new notion of HQFTs…

Given a closed monotone symplectic manifold $M$, we define certain characteristic cohomology classes of the free loop space $L \text {Ham}(M, \omega)$ with values in $QH_* (M)$, and their $S^1$ equivariant version. These classes generalize…

Inspired by an extension of Wiener's lemma on the relation of measures $\mu$ on the unit circle and their Fourier coefficients $\widehat{\mu}(k_n)$ along subsequences $(k_n)$ of the natural numbers by Cuny, Eisner and Farkas [CEF19,…

For each representative $\mathfrak{B}$ of a bordism class in the free loop space of a manifold, we associate a moduli space of finite length Floer cylinders in the cotangent bundle. The left end of the Floer cylinder is required to be a…

We study the homology of free loop spaces via techniques arising from the theory of topological coHochschild homology (coTHH). Topological coHochschild homology is a topological analogue of the classical theory of coHochschild homology for…

We show that the free construction from multicategories to permutative categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induced functor between categories of algebras is an equivalence…

We consider the Hurwitz spaces of ramified coverings of $\mathbb{P}^1$ with prescribed ramification profile over the point at infinity. By means of a particular symmetric bidifferential on a compact Riemann surface, we introduce…

Poisson boundary is a measurable $\Gamma$-space canonically associated with a group $\Gamma$ and a probability measure $\mu$ on it. The collection of all measurable $\Gamma$-equivariant quotients, known as $\mu$-boundaries, of the Poisson…

We show that the orbit equivalence relation of a free action of a locally compact group is hyperfinite (\`a la Connes-Feldman-Weiss) precisely when it is 'hypercompact'. This implies an uncountable version of the Ornstein-Weiss Theorem and…