Related papers: Twisted IBL-infinity-algebra and string topology: …
Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to…
Motivated by the problem of constructing explicit geometric string structures, we give a rigid model for bundle 2-gerbes, and define connective structures thereon. This model is designed to make explicit calculations easier in applications…
The geometry of nonholonomic bundle gerbes, provided with nonlinear connection structure, and nonholonomic gerbe modules is elaborated as the theory of Clifford modules on nonholonomic manifolds which positively fail to be spin. We explore…
Incommensurately twisted graphene bilayers are described by long-wavelength theories, but to date such theories exist only at small angles of interlayer rotation. We construct a long wavelength theory without such a restriction, instead…
The $R^2 F^{2g-2}$ terms of Type IIA strings on Calabi-Yau 3-folds, which are given by the corresponding topological string amplitudes (a worldsheet instanton sum for all genera), are shown to have a simple M-theory interpretation. In…
The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using…
We prove `twisted' versions of Kirchhoff's network theorem and Kirchhoff's matrix-tree theorem on connected finite graphs. Twisting here refers to chains with coefficients in a flat unitary line bundle.
Twisted multilayer systems, encompassing materials like twisted bilayer graphene (TBG), twisted trilayer graphene, and twisted bilayer transition metal dichalcogenides, have garnered significant attention in condensed matter physics.…
We investigate how topological entanglement of Chern-Simons theory is captured in a string theoretic realization. Our explorations are motivated by a desire to understand how quantum entanglement of low energy open string degrees of freedom…
This paper studies the structure of graphs with given tree-width and excluding a fixed complete bipartite subgraph, which generalises the bounded degree setting. We give a new structural description of such graphs in terms of so-called…
We study Thurston equivalence classes of quadratic post-critically finite branched coverings. For these maps, we introduce and study invariant spanning trees. We give a computational procedure for searching for invariant spanning trees.…
We study degree spectra of structures with respect to the bi-embeddability relation. The bi-embeddability spectrum of a structure is the family of Turing degrees of its bi-embeddable copies. To facilitate our study we introduce the notions…
We construct string topology operations in twisted K-theory. We study the examples given by symplectic Grassmannians, computing the twisted K-theory of the loop spaces of quaternionic projective spaces in detail. Via the work of…
Motivated by logarithmic conformal field theory and Gromov-Witten theory, we introduce a notion of a twisted module of a vertex algebra under an arbitrary (not necessarily semisimple) automorphism. Its main feature is that the twisted…
In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic…
The construction of link polynomials associated with finite dimensional representations of ribbon quasi-Hopf algebras is discussed in terms of the formulation of an appropriate Markov trace. We then show that this Markov trace is invariant…
Adapting a result of Bazhenov, Kalimullin, and Yamaleev, we show that if a Turing degree $\textbf{d}$ is the degree of categoricity of a computable structure $\mathcal{M}$ and is not the strong degree of categoricity of any computable…
This article is devoted to the investigation of wrap groups of connected fiber bundles over the fields of real $\bf R$, complex $\bf C$ numbers, the quaternion skew field $\bf H$ and the octonion algebra $\bf O$. Cohomologies of wrap groups…
In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber a matrix algebra. We also introduce some generalization of the Brauer group in the topological context and show that any its element…
Let $R$ be a polynomial ring in $m$ variables over a field of characteristic zero. We classify all rank $n$ twisted generalized Weyl algebras over $R$, up to $\mathbb{Z}^n$-graded isomorphisms, in terms of higher spin 6-vertex…