Related papers: Lump dynamics in the CP^1 model on the torus

The most fruitful approach to studying low energy soliton dynamics in field theories of Bogomol'nyi type is the geodesic approximation of Manton. In the case of vortices and monopoles, Stuart has obtained rigorous estimates of the errors in…

For non-compact, locally symmetric moduli spaces M, the set of geodesics and the geometry of the boundary can be completely characterised using group theory. In particular, geodesics that asymptote to a given infinite distance boundary…

We study nearly parallel $\mathrm{G}_{2}$-structures with a three-torus symmetry via multi-moment map techniques. An effective three-torus action on a nearly parallel $\mathrm{G}_{2}$-manifold yields a multi-moment map. The torus acts…

Let ${\mathcal G}$ be a locally compact group. In continuation of our studies on the first and second duals of measure algebras by the use of the theory of generalised functions, here we study the C$^*$-subalgebra $GL_0({\mathcal G})$ of…

In this paper, we construct infinitely many diffeomorphisms of a Joyce manifold $M$ which achieve Yomdin's homological lower bound for topological entropy, imitating a recent construction of Farb-Looijenga for K3 surfaces. Moreover,…

The geodesic structure is very closely related to the trace of the Laplace operator, involved in the calculation of the expectation value of the energy momentum tensor in Universes with non trivial topology. The purpose of this work is to…

We study the topology of the tropical moduli space parametrizing stable tropical curves of genus g with n marked points in which the bounded edges have total length 1, and prove that it is highly connected. Using the identification of this…

Let $G$ be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let $\pi$ be the fundamental group of an orientable (real) surface $M$ with a finite number of punctures, and let $\bold C$ be a family of…

We study the heterotic G$_2$-system on 7-dimensional 2-step nilmanifolds $M=\Gamma\backslash N$ endowed with principal torus bundles. We first prove that every invariant G$_2$-structure solving the system must be coclosed (under an…

Given a sublinear function $\kappa$, $\kappa$-Morse boundaries $\pka X$ of proper \CAT spaces are introduced by Qing, Rafi and Tiozzo. It is a topological space that consists of a large set of quasi-geodesic rays and it is…

We study the topology of the moduli space of unramified $\mathbb{Z}/p$-covers of tropical curves of genus $g \geq 2$, where $p$ is a prime number. We use recent techniques by Chan--Galatius--Payne to identify contractible subcomplexes of…

The double torus provides a relativistic model for a closed 2D cosmos with topology of genus 2 and constant negative curvature. Its unfolding into an octagon extends to an octagonal tessellation of its universal covering, the hyperbolic…

Let L be a D-dimensional submanifold of a 2D-dimensional exact symplectic manifold (M, w) and let f be a symplectic diffeomorphism onf M. In this article, we deal with the link between the dynamics of f restricted to L and the geometry of L…

We study the nonrigid dynamics induced by the standard birational actions of the split unitary groups $G=O_{o}\left( n,n\right) $, $SU\left( n,n\right) $ and $Sp\left( n,n\right) $ on the compact classical Lie groups $M=SO_{n}$, $% U_{n}$…

We study a space of genus $g$ stable, $n$-marked tropical curves with total edge length $1$. Its rational homology is identified both with top-weight cohomology of the complex moduli space $M_{g,n}$ and with the homology of a marked version…

The gauged sigma model with target $\mathbb{P}^1$, defined on a Riemann surface $\Sigma$, supports static solutions in which $k_+$ vortices coexist in stable equilibrium with $k_-$ antivortices. Their moduli space is a noncompact complex…

We investigate the low-energy dynamics of the BPS solitons of the noncommutative CP^1 model in 2+1 dimensions using the moduli space metric of the BPS solitons. We show that the dynamics of a single soliton coincides with that in the…

We study topological lumps supported by the second homotopy group $\pi_2(S^2) \simeq {\mathbb Z}$ in a gauged $O(3)$ model without any potential term coupled with a (non)dynamical $U(1)$ gauge field. It is known that gauged-lumps are stable…

Let $ \mathfrak{M}$ be the moduli space of torsion free $ G_2$ structures on a compact 7-manifold $ M$, and let $ \mathfrak{M}_1 \subset \mathfrak{M}$ be the $ G_2$ structures with volume($M$) $=1$. The cohomology map $ \pi^3: \mathfrak{M}…

This paper contains a purely topological theorem and a geometric application. The topological theorem states that if M is a simple closed orientable 3-manifold such that \pi_1(M) contains a genus g surface group and H_1(M;Z/2Z) has rank at…