Related papers: Topological pressure for holomorphic correspondenc…

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

We study the open/closed correspondence for the projective line via mirror symmetry. More explicitly, we establish a correspondence between the generating function of disk Gromov-Witten invariants of the complex projective line…

Translation surfaces can be defined in an elementary way via polygons, and arise naturally in in the study of various basic dynamical systems. They can also be defined as Abelian differentials on Riemann surfaces, and have moduli spaces…

The notion of higher-order topological phases can have interesting generalizations to systems with subsystem symmetries that exhibit fractonic dynamics for charged excitations. In this work, we systematically study the higher-order…

Given a closed Riemannian manifold, we show how to close an orbit of the geodesic flow by a small perturbation of the metric in the $C^1$ topology.

Topology of the spatial coherence function is considered in details. The phase singularity (coherence vortices) structures of coherence function are classified by Hopf index and Brouwer degree in topology. The coherence flux quantization…

We generalize the holographic correspondence between topological gravity coupled to an abelian Chern-Simons theory in three dimensions and an ensemble average of Narain's family of massless free bosons in two dimensions, discovered by…

We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.

It has long been suggested that the mid-latitude atmospheric circulation possesses what has come to be known as `weather regimes', loosely categorised as regions of phase space with above-average density and/or extended persistence. Their…

We define new topological invariants for Anosov representations and study them in detail for maximal representations of the fundamental group of a closed oriented surface into the symplectic group.

In a non-compact context the first natural step in the search for periodic orbits of a hamiltonian flow is to detect bounded ones. In this paper we show that, in a non-compact setting, certain algebraic topological constraints imposed to a…

We derive a general closed expression for the local pressure exerted onto the corrugated walls of a channel confining a fluid medium. When the fluid medium is at equilibrium the local pressure is a functional of the shape of the walls. It…

Let $D\subset \C^n,$ $G\subset \C^m$ be open sets, let $A$ (resp. $B$) be a subset of the boundary $\partial D$ (resp. $\partial G$) and let $W$ be the 2-fold boundary cross $((D\cup A)\times B)\cup (A\times(B\cup G)).$ An open subset…

A topological pump enables robust transport of quantized particles when the system parameters are varied in a cyclic process. In previous studies, topological pump was achieved inhomogeneous systems guaranteed by a topological invariant of…

We track the trajectories of individual horocycles on the modular surface. Our tracking is constructive, and we thus \emph{effectively} establish topological transitivity and even line-transitivity for the horocyclic flow. We also describe…

This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.

The classical theta correspondence establishes a relationship between automorphic representations on special orthogonal groups and automorphic representations on symplectic groups or their double covers. This correspondence is achieved by…

The primary goal of this paper is to find a homotopy theoretic approximation to moduli spaces of holomorphic maps Riemann surfaces into complex projective space. There is a similar treatment of a partial compactification of these moduli…

We identify as topological spheres those complete submanifolds lying with any codimension in hyperbolic space whose Ricci curvature satisfies a lower bound contingent solely upon the length of the mean curvature vector of the immersion.

The homology of a 2-colored dioperad of decorated Riemann surfaces, relevant to open-closed string field theory, is computed. The structure it describes is realized in an open-closed setting of string topology via an action at the level of…