Related papers: Free loop spaces and the Cauchy--Frobenius Lemma
We consider three dimensional gravity with a positive cosmological constant and non- zero gravitational Chern-Simons term. This theory has inflating de Sitter solutions and local metric degrees of freedom. The Euclidean signature partition…
We construct a class of infinite-dimensional Frobenius manifolds on the space of pairs of certain even functions meromorphic inside or outside the unit circle. Via a bi-Hamiltonian recursion relation, the principal hierarchies associated to…
Previous work (Pradines, 1966, Aof and Brown, 1992) has given a setting for a holonomy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This…
Motivated by a recent paper of Fock and Rosly \cite{FoRo} we describe a mathematically precise quantization of the Hamiltonian Chern-Simons theory. We introduce the Chern-Simons theory on the lattice which is expected to reproduce the…
The correct Hamiltonian for an extended Hubbard model with quantum group symmetry as introduced by A. Montorsi and M. Rasetti is derived for a D-dimensional lattice. It is shown that the superconducting SUq(2) holds as a true quantum…
We investigate algebraic and compositional properties of abstract multiway rewriting systems, which are archetypical structures underlying the formalism of the Wolfram model. We demonstrate the existence of higher homotopies in this class…
We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for…
Goodwillie's proof of the Blakers-Massey Theorem for $n$-cubes relies on a lemma whose proof invokes transversality. The rest of his proof follows from general facts about cubes of spaces and connectivities of maps. We present a purely…
We consider the nonrotating isolated horizon as an inner boundary of a four-dimensional asymptotically flat spacetime region. Due to the symmetry of the isolated horizon, it turns out that the boundary degrees of freedom can be described by…
We derive an asymptotic expansion for a Wiener-Hopf determinant arising in the problem of counting one-dimensional free fermions on a line segment at zero temperature. This expansion is an extension of the result in the theory of Toeplitz…
Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend to homotopy colimits of 2-functors lower categorical…
We establish a higher Freudenthal suspension theorem and prove that the derived fundamental adjunction comparing spaces with coalgebra spaces over the homotopical iterated suspension-loop comonad, via iterated suspension, can be turned into…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
We develop a homotopy theory of $L_\infty$ algebras based on the Lawrence-Sullivan construction, a complete differential graded Lie algebra which, as we show, satisfies the necessary properties to become the right cylinder in this category.…
We provide, among other things: (i) a Bousfield--Kan formula for colimits in $\infty$-categories (generalizing the 1-categorical formula for a colimit as a coequalizer of maps between coproducts); (ii) $\infty$-categorical generalizations…
The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed. Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an…
In this paper we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearisation of the general conformal field equations near spacelike infinity, which is only well-defined in Friedrich's…
Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\mathsf{Mod}(T)$ to be homotopically equivalent to $\mathbb{CP}^\infty$. In particular,…
We use Fuchsian Reduction to construct singular solutions of Einstein's equations which belong to the class of Gowdy spacetimes. The solutions have the maximum number of arbitrary functions. Special cases correspond to polarized, or other…
For the Bianchi type I space-time (vacuum or with a massless scalar field), the loop quantum cosmology bounce can be viewed as a rapid transition between two classical solutions, with a simple transformation rule relating the Kasner…