Related papers: The monochromatic Hopf invariant

We study the order of affine and linear invariant families of planar harmonic mappings in the unit disk and determine the order of the family of mappings with bounded Schwarzian norm. The result shows that finding the order of the class…

The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…

Let $A$ be a finite abelian $p$ group of rank at least $2$. We show that $E^0(BA)/I_{tr}$, the quotient of the Morava $E$-cohomology of $A$ by the ideal generated by the image of the transfers along all proper subgroups, contains…

Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of…

We give invariants of flat bundles over 4-manifolds generalizing a result by Chaidez, Cotler, and Cui (Alg. \& Geo. Topology '22). We utilize a structure called a Hopf $G$-triplet for $G$ a group, which generalizes the notion of a Hopf…

In this article we describe a new inductive approach to compute the chromatic polynomial of simple graphs and the characteristic polynomial of central hyperplane arrangements.

We calculate the motivic stable homotopy groups of the two-complete sphere spectrum after inverting multiplication by the Hopf map eta over fields of cohomological dimension at most 2 with characteristic different from 2 (this includes the…

We associate an invariant called the completed Tate cohomology to a filtered circle-equivariant spectrum and a complex oriented cohomology theory. We show that when the filtered spectrum is the spectral symplectic cohomology of a Liouville…

In this paper we present a Maple library (MOPs) for computing Jack, Hermite, Laguerre, and Jacobi multivariate polynomials, as well as eigenvalue statistics for the Hermite, Laguerre, and Jacobi ensembles of Random Matrix theory. We also…

In this article we show how to compute the chromatic quasisymmetric function of indifference graphs from the modular law introduced by Guay-Paquet. We provide an algorithm which works for any function that satisfies this law, such as…

We show that the twisted Bredon-Illman cohomology defined by Mukherjee-Mukherjee applied to compact Lie group action groupoids is Morita-invariant. This cohomology uses coefficient systems twisted over the discrete tom Dieck equivariant…

We give a Hopf-algebraic formulation of the $R^*$-operation, which is a canonical way to render UV and IR divergent Euclidean Feynman diagrams finite. Our analysis uncovers a close connection to Brown's Hopf algebra of motic graphs. Using…

We consider the polynomial algebra $\mathbb{C}[\mathbf{z}]:=\mathbb{C}[z_1,\,z_2,\,z_3]$ and the polynomial $f:=z_1^3+z_2^3+z_3^3+3qz_1z_2z_3$, where $q\in \mathbb{C}$. Our aim is to compute the Hochschild homology and cohomology of the…

We outline the construction of invariants of Hamiltonian group actions on symplectic manifolds. These invariants can be viewed as an equivariant version of Gromov-Witten invariants. They are derived from solutions of a PDE involving the…

Let $M$ be a smooth manifold and $\Gamma$ a group acting on $M$ by diffeomorphisms; which means that there is a group morphism $\rho:\Gamma\rightarrow \mathrm{Diff}(M)$ from $\Gamma$ to the group of diffeomorphisms of $M$. For any such…

We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler--Poincar\'e equations defined on the Virasoro-Bott group, by using the inverse map (also called…

In this paper, we first introduce the concept of Rota-Baxter family BiHom-$\Omega$-associative algebras, then we define the cochain complex of BiHom-$\Omega$-associative algebras and verify it via Maurer-Cartan methods. Next, we further…

We give here the Hopf algebra structure describing the noncommutative renormalization of a recently introduced translation-invariant model on Moyal space. We define Hochschild one-cocyles $B_+^\gamma$ which allows us to write down the…

For every stable presentably symmetric monoidal $\infty$-category $\mathcal{C}$ we use the Koszul duality between the spectral Lie operad and the cocommutative cooperad to construct an enveloping Hopf algebra functor $\mathcal{U}:…

For studying the meromorphic degeneration of complex dynamics, the theory of hybrid spaces, introduced by Boucksom, Favre and Jonsson, is known to be a strong tool. In this paper, we apply this theory to the dynamics of H\'enon maps. For a…