Related papers: Non-differentiable irrational curves for $C^1$ twi…

Let $\Gamma$ denote a finite, simple and connected graph. Fix a vertex $x$ of $\Gamma$ which is not a leaf and let $T=T(x)$ denote the Terwilliger algebra of $\Gamma$ with respect to $x$. Assume that the unique irreducible $T$-module with…

We characterize connected tetravalent graphs $\Gamma$ which admit groups $M<H$ of automorphisms such that $\Gamma$ is $M$-half-arc-transitive and $H$-arc-transitive. Examples for each case are constructed, including a counter-example to a…

A group $G$ of permutations of a set $\Omega$ is {\em primitive} if it acts transitively on $\Omega$, and the only $G$-invariant equivalence relations on $\Omega$ are the trivial and universal relations. A graph $\Gamma$ is {\em primitive}…

A sequence of constant mean curvature surfaces $\Sigma_j$ with mean curvature $H_j \to \infty$ in a three-dimensional manifold $M$ condenses to a compact and connected graph $\Gamma$ consisting of a finite union of curves if $\Sigma_j$ is…

In this note we make progress toward a conjecture of Durham--Fanoni--Vlamis, showing that every infinite-type surface with finite-invariance index 1 and no nondisplaceable compact subsurfaces fails to have a good curve graph, that is, a…

Let $\Gamma$ be a countable group and $(X, \Gamma)$ a compact topological dynamical system. We study the question of the existence of an intermediate $C^*$-subalgebra $\mathcal{A}$ $$C^{*}_{r}(\Gamma)<\mathcal{A}<C(X)\rtimes_r\Gamma,$$…

The possibility of noncommutative topological gravity arising in the same manner as Yang-Mills theory is explored. We use the Seiberg-Witten map to construct such a theory based on a SL(2,C) complex connection, from which the Euler…

We present an approach to Gromov-Witten invariants that works on arbitrary (closed) symplectic manifolds. We avoid genericity arguments and take into account singular curves in the very formulation. The method is by first endowing mapping…

Let $T$ be a graph in a compact, orientable 3--manifold $M$ and let $\Gamma$ be a subgraph. $T$ can be placed in bridge position with respect to a Heegaard surface $H$. We show that if $H$ is what we call $(T,\Gamma)$-c-weakly reducible in…

Let $G$ be a simple topological graph and let $\Gamma$ be a polyline drawing of $G$. We say that $\Gamma$ \emph{partially preserves the topology} of $G$ if it has the same external boundary, the same rotation system, and the same set of…

We construct a parabolic entire minimal graph $S$ over a finite topology complete Riemannian surface $\Sigma$ of curvature $-1$ and infinite area (thus of non-parabolic conformal type). The vertical projection of this graph yields a…

We introduce uniformly vertex-transitive graphs as vertex-transitive graphs satisfying a stronger condition on their automorphism groups, motivated by a problem which arises from a Sinkhorn-type algorithm. We use the derangement graph…

We classify algebraic curves in $\mathbb{CP}^{n}$ ($n \geq 2$) that are invariant under an infinite subgroup of $\operatorname{PGL}(n+1,\mathbb{C})$. In particular, we prove that any irreducible, non-degenerate, one-dimensional algebraic…

We investigate conditions on a graph $C^*$-algebra for the existence of a faithful semifinite trace. Using such a trace and the natural gauge action of the circle on the graph algebra, we construct a smooth $(1,\infty)$-summable semfinite…

Motivated by Nirenberg's problem on isometric rigidity of tight surfaces, we study closed asymptotic curves $\Gamma$ on negatively curved surfaces $M$ in Euclidean $3$-space. In particular, using C\u{a}lug\u{a}reanu's theorem, we obtain a…

We prove that any two $C^3$ critical circle maps with the same irrational rotation number of bounded type and the same odd criticality are conjugate to each other by a $C^{1+\alpha}$ circle diffeomorphism, for some universal $\alpha>0$.

Given an irreducible lattice $\Gamma$ in the product of higher rank simple Lie groups, we prove a co-finiteness result for the $\Gamma$-invariant von Neumann subalgebras of the group von Neumann algebra $\mathcal{L}(\Gamma)$, and for the…

For a manifold M we define a structure on the group action of Diff(M) on the smooth functions on M which reduces to the usual differential geometry upon differentiation at zero along the one-parameter groups of Diff(M). This ``integrated…

Every separable nondegenerate C*-correspondence over a commutative C*-algebra with discrete spectrum is isomorphic to a graph correspondence.

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…