Related papers: Topological aspects of the dynamical moduli space …

In this paper, we establish a number of results about the topology of the leaves of a closed singular Riemannian foliation $(M,\fol)$. If $M$ is simply connected, we prove that the leaves are finitely covered by nilpotent spaces, and…

Let X be a compact nonsingular real algebraic variety. We prove that if a continuous map from X into the unit p-sphere is homotopic to a continuous rational map, then, under certain assumptions, it can be approximated in the compact-open…

The hyperbolic components in the moduli space ${M}_d$ of degree $d\geq2$ rational maps are mysterious and fundamental topological objects. For those in the connectedness locus, they are known to be the finite quotients of the Euclidean…

Let M be a Riemann surface with boundary $\partial M$ and genus greater than zero. Let $\Gamma$ be the mapping class group of M fixing $\partial M$. The group $\Gamma$ acts on ${\mathcal M}_{\mathcal C} = \Hom_{\mathcal…

We consider the extension of classical 2-dimensional topological quantum field theories to Klein topological quantum field theories which allow unorientable surfaces. We approach this using the theory of modular operads by introducing a new…

In this paper we study the topology of the spaces Hol(M,P{n},k) of (basepoint preserving) holomorphic maps of a given degree k from a Riemann surface M of genus g>0 into the n-th complex projective space P{n}, n>0. Using symmetric products…

The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy…

Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…

The real locus of the moduli space of stable genus-zero curves with marked points, $\overline{{\mathcal M}_{0,{n+1}}}({\mathbb R})$, is known to be a smooth manifold and is the Eilenberg-MacLane spaces for the so-called pure Cactus groups.…

We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of…

We consider two cycles on the moduli space of compact type curves and prove that they coincide. The first is defined by pushing forward the virtual fundamental classes of spaces of relative stable maps to an unparameterized rational curve,…

This is an expository article, originally written in Japanese, on a dynamical system over a non-archimedean field. The main viewpoint is from complex and non-archimedean potential theories. After quickly introducing the Berkovich projective…

Working over an algebraically closed field $k$ of characteristic $0$, we show that the motivic stable homotopy groups of the sphere spectrum can be determined entirely from the motivic homotopy groups of the $p$-completed sphere spectra and…

In this paper, we study the dynamical uniform boundedness principle over a family of rational maps with certain nontrivial automorphisms. Specifically, we consider a family of rational maps of an arbitrary degree $d\ge 2$ whose automorphism…

We study holomorphic $(n+1)$-chains $E_n\to E_{n-1} \to >... \to E_0$ consisting of holomorphic vector bundles over a compact Riemann surface and homomorphisms between them. A notion of stability depending on $n$ real parameters was…

Inspired by his vanishing results of tautological classes and by Harer's computation of the virtual cohomological dimension of the mapping class group, Looijenga conjectured that the moduli space of smooth Riemann surfaces admits a…

We construct moduli spaces of framed logarithmic connections and also moduli spaces of framed parabolic connections. It is shown that these moduli spaces possess a natural algebraic symplectic structure. We also give an upper bound of the…

The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…

This work serves as an opening and basis of an ongoing program investigating topological and geometric aspects of the moduli space of smooth fiberings on a manifold. The present paper focuses on the algebraic and differential topology of…

This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…