Related papers: Twisting cochains and higher torsion
For the first time, robust superconductivity has been independently observed in twisted WSe$_2$ bilayers by two separate groups [Y. Xia et al., arXiv:2405.14784; Y. Guo et al., arXiv:2406.03418.]. In light of this, we explore the…
We give a geometric interpretation of sheaf cohomology for higher degrees n in terms of torsors on the member of degree d=n-1 in hypercoverings of type r=n-2, endowed with an additional data, the so-called rigidification. This generalizes…
In this note we propose that D-brane charges, in the presence of a topologically non-trivial B-field, are classified by the K-theory of an infinite dimensional C^*-algebra. In the case of B-fields whose curvature is pure torsion our…
A d-contraction is a d-tuple $(T_1,...,T_d)$ of mutually commuting operators acting on a common Hilbert space H such that $ \|T_1\xi_1+T_2\xi_2+... +T_d\xi_d\|^2\leq \|\xi_1\|^2+\|\xi_2\|^2+...+\|\xi_d\|^2 $ for all…
Recently it has been shown that D-branes in orientifolds are not always described by equivariant Real K-theory. In this paper we define a previously unstudied twisted version of equivariant Real K-theory which gives the D-brane spectrum for…
We study the homotopy aspects of the twisted Chern classes of torsion bundle gerbe modules. Using Sullivan's rational homotopy theory, we realize the twisted Chern classes at the level of classifying spaces. The construction suggests a…
Let $A$ be a $k$-algebra where $k$ is an algebraically closed field and $G$ be a finite abelian group for which the characteristic of $k$ does not divide $|G|$. If $G$ acts on $A$ by $k$-algebra automorphisms then the action induces a…
We specialise a recently introduced notion of generalised dinaturality for functors $T : (\mathcal{C}^\text{op})^p \times \mathcal{C}^q \to \mathcal{D}$ to the case where the domain (resp., codomain) is constant, obtaining notions of ends…
Many of the important phases observed in twisted transition metal dichalcogenide homobilayers are driven by short-range interactions, which should be captured by a local tight binding description since no Wannier obstruction exists for…
It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…
We recapture Douglas' framework for twisted parametrized stable homotopy theory in the language of $\infty$- categories. A twisted spectrum is essentially a section of a bundle of presentable stable $\infty$-categories whose fiber is the…
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…
We provide a finite-dimensional model of the twisted K-group twisted by any degree three integral cohomology class of a CW complex. One key to the model is Furuta's generalized vector bundle, and the other is a finite-dimensional…
Motivated by recent experimental observations of opposite Chern numbers in $R$-type twisted MoTe$_2$ and WSe$_2$ homobilayers, we perform large-scale density-functional-theory (DFT) calculations with machine learning force fields to…
Cosine-shaped bands that occur in DFT-based electronic band structures for MgB2 are further analyzed with calculations along reciprocal directions parallel to the high symmetry G-A direction at regular intervals along G-M. Band degeneracies…
We investigate the formation of helical multifilament bundles and the torque required to achieve them as a function of applied twist. Hyperelastic filaments with circular cross sections are mounted parallel in a uniform circle onto…
In a recent paper, Lai and Rohatgi proved a "shuffling theorem" for lozenge tilings of a hexagon with "dents" (i.e., missing triangles). Here, we shall point out that this follows immediately from the enumeration of Gelfand--Tsetlin…
In a previous paper by the authors, we found some patterns in link diagrams that give rise to torsion elements of order two in their Khovanov homology. In this paper we extend these results by providing new torsion patterns. Many of the…
We investigate experimentally and model the mechanical response of a soft Hookean ribbon submitted to large twist $\eta$ and longitudinal tension $T$, under clamped boundary conditions. We derive a formula for the torque $M$ using the \FvK…
Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial version of a differential…