Related papers: $t$-adic symmetrization map on harmonic algebra

We use filtrations of the Grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a Riemann surface, and so all harmonic maps from the 2-sphere, to the unitary group for a general class…

In this paper, we discuss the associated family of harmonic maps $\mathcal{F}: M \rightarrow G/K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type which are either algebraic or totally symmetric. These…

We study harmonic morphisms of graphs as a natural discrete analogue of holomorphic maps between Riemann surfaces. We formulate a graph-theoretic analogue of the classical Riemann-Hurwitz formula, study the functorial maps on Jacobians and…

In a recent paper the first and the third authors introduced the notion of horizontal \alpha-harmonic map, with respect to a given C^1 planes distribution P_T on all R^m. The goal of this paper is to investigate compactness and quantization…

For an arbitrary Dirac-harmonic map $(\phi,\psi)$ between compact oriented Riemannian surfaces, we shall study the zeros of $|\psi|$. With the aid of Bochner-type formulas, we explore the relationship between the order of the zeros of…

We study semifinite harmonic functions on arbitrary branching graphs. We give a detailed exposition of an algebraic method which allows one to classify semifinite indecomposable harmonic functions on some multiplicative branching graphs.…

In this paper we study the operator inequality \phi(X)\leq X and the operator equation \phi(X)= X, where \phi is a w^*-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one…

Let $\phi \colon \Gamma_2 \rightarrow \Gamma_1$ be a harmonic morphism of connected graphs. We show that an arithmetical structure on $\Gamma_1$ can be pulled back via $\phi$ to an arithmetical structure on $\Gamma_2$. We then show that…

Let $\zeta$ and $\eta$ be distinct points on the unit circle and suppose that $\phi$ is a linear-fractional self-map of the unit disk D, not an automorphism, with $\phi(\zeta)=\eta$. We describe the C*-algebra generated by the associated…

Let $C$ be a general unital AH-algebra and let $A$ be a unital simple $C^*$-algebra with tracial rank at most one. Suppose that $\phi, \psi: C\to A$ are two unital monomorphisms. We show that $\phi$ and $\psi$ are approximately unitarily…

\textit{Harmonic amoebas} are generalisations of amoebas of algebraic curves immersed in complex tori. Introduced in \cite{Kri}, the consideration of such objects suggests to enlarge the scope of tropical geometry. In the present paper, we…

Let $(\Sigma,p)$ be a pointed Riemann surface of genus $g\geq 1$. For any integer $k\geq 1$, we parametrize the space of meromorphic quadratic differentials on $\Sigma$ with a pole of order $(k+2)$ at $p$, having a connected critical graph…

In this paper, we generalize the combinatorial Laplace operator of Horak and Jost by introducing the $\phi$-weighted coboundary operator induced by a weight function $\phi$. Our weight function $\phi$ is a generalization of Dawson's…

We classify all harmonic maps with finite uniton number from a Riemann surface into an arbitrary compact simple Lie group $G$, whether $G$ has trivial centre or not, in terms of certain pieces of the Bruhat decomposition of the group…

Given a CW-complex A we define an `A-shaped' homology theory which behaves nicely towards A-homotopy groups allowing the generalization of many classical results. We also develop a relative version of the Federer spectral sequence for…

For fibred boundary and fibred cusp metrics, Hausel, Hunsicker, and Mazzeo identified the space of $L^2$ harmonic forms of fixed degree with the images of maps between intersection cohomology groups of an associated stratified space…

We determine the algebra of holonomy symmetries of sigma models propagating on supersymmetric heterotic backgrounds with a non-compact holonomy group. We demonstrate that these close as a W-algebra, which in turn is specified by a Lie…

We introduce and study weak-2-local symmetric maps between C$^*$-algebras $A$ and $B$ as non necessarily linear nor continuous maps $\Delta: A\to B$ such that for each $a,b\in A$ and $\phi\in B^{*}$, there exists a symmetric linear map…

We construct a comparison map between the gamma homology theory of Robinson and Whitehouse and the symmetric homology theory of Fiedorowicz and Ault in the case of an augmented, commutative algebra over a unital commutative ground ring.

In a continuation of our previous work, we outline a theory which should lead to the construction of a universal pre-building and versal building with a $\phi$-harmonic map from a Riemann surface, in the case of two-dimensional buildings…