Related papers: Cohomology classes of admissible normal functions

We construct nontrivial cohomology classes of the space $Imb(S^1,\R^n)$ of imbeddings of the circle into $\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we…

We classify generic coadjoint orbits for symplectomorphism groups of compact symplectic surfaces with or without boundary. We also classify simple Morse functions on such surfaces up to a symplectomorphism.

Let X be a smooth projective curve over a perfect field k of positive characteristic. This work investigates the relationship between stratified cohomology and group cohomology of the stratified fundamental group of X.

This manuscript develops a geometric approach to ordinary cohomology of smooth manifolds, constructing a cochain complex model based on co-oriented smooth maps from manifolds with corners. Special attention is given to the pull-back product…

We express the rational cohomology of the unordered configuration space of a compact oriented manifold as a representation of its mapping class group in terms of a weight-decomposition of the rational cohomology of the mapping space from…

This article presents conditions under which the skewed version of immaculate noncommutative symmetric functions are nonzero. The work is motivated by the quest to determine when the matrix definition of a skew immaculate function aligns…

Let $S$ and $T$ be smooth projective varieties over an algebraically closed field. Suppose that $S$ is a surface admitting a decomposition of the diagonal. We show that, away from the characteristic of $k$, if an algebraic correspondence $T…

Johnson's characterization of amenable groups states that a discrete group $\Gamma$ is amenable if and only if $H_b^{n \geq 1}(\Gamma; V) = 0$ for all dual normed $\mathbb{R}[\Gamma]$-modules V. In this paper, we extend the previous result…

We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…

A fast algorithm for counting intersections of two normal curves on a triangulated surface is proposed. It yields a convenient way for treating mapping class groups of punctured surfaces by presenting mapping classes by matrices, and the…

The notion of acceptable bundles plays a fundamental role in the Simpson--Mochizuki theory. We study acceptable bundles on a partially punctured polydisk in detail. While this article is primarily expository, it also presents new arguments…

We show that a normal coaction of a discrete group on an operator algebra extends to a normal coaction on the C*-envelope. This resolves an open problem attempted by several experts in the area, and provides a more direct proof of a…

These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…

Standard combinatorial construction, due to Kontsevich, associates to any $\ai$-algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We propose an…

We define a cotriple (co)homology of crossed modules with coefficients in a $\pi_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with…

Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…

This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…

We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show this (co)homology, called Hopf--Hochschild (co)homology, can also be…

We study bijections between the positive cones of spaces of continuous functions vanishing at infinity that satisfy a norm additive condition. Such maps arise naturally in the study of nonlinear functional equations and norm-preserving…

We show that a map between complex-analytic manifolds, at least one of which is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain…