Related papers: Topological constructions of tensor fields on modu…

This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a…

We show that there exists a fine moduli space for torsion-free sheaves on a projective surface, which have a "good framing" on a big and nef divisor. This moduli space is a quasi-projective scheme. This is accomplished by showing that such…

We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…

The rings of linear continuous operators on the topological spaces of $\mathfrak{G}$-zero maps were described, where $\mathfrak{G}$ is a filter on a set with an involution. This applies to modules of formal series with well ordered support…

Distributional tensor fields can be regarded as multilinear mappings with distributional values or as (classical) tensor fields with distributional coefficients. We show that the corresponding isomorphisms hold also in the bornological…

We describe the structure of the top tautological group in the cohomology of the moduli space of smooth genus $g$ curves with $n$ marked points.

In the time evolution of fluids, the topologies of fluids can be changed by the creations and annihilations of singular points and by switching combinatorial structures of separatrices. In this paper, to describe the possible generic time…

This article is concerned with moduli spaces of connections on bundles on Riemann surfaces, where the structure group of the bundle may vary in different regions of the surface. Here we will describe such moduli spaces as complex symplectic…

In this paper, we prove a theorem about embedding of some partially ordered topological spaces in topological hyperspaces equipped with Fell topology. Then we give some examples to show that the map defining the embedding may not be…

For a vertex operator algebra $V$, one may naturally define spaces of conformal blocks following a construction of Frenkel-Ben-Zvi generalized by Damiolini-Gibney-Tarasca. If $V$ is strongly rational, these spaces of conformal blocks form…

A class of effective field theories for moduli or collective coordinates on solitons of generic shapes is constructed. As an illustration, we consider effective field theories living on solitons in the O(4) non-linear sigma model with…

We investigate topological properties of the moduli space of spin structures over genus two curves. In particular, we provide a combinatorial description of this space and give a presentation of the (rational) cohomology ring via generators…

Let X be a smooth projective curve of genus at least two over the complex numbers. A pair (E,\phi) over X consists of an algebraic vector bundle E over X and a holomorphic section \phi of E. There is a concept of stability for pairs which…

We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson-Uhlenbeck compactification and explain how…

In this paper we give construct good moduli spaces for constructible sheaves and Stokes functors. Derived enhancement of such are also considered.

We show how locally smooth actions of compact Lie groups on a manifold $X$ can be used to obtain new upper bounds for the topological complexity $\TC(X)$, in the sense of Farber. We also obtain new bounds for the topological complexity of…

In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…

In this mostly expository paper we review several known results about the cohomology of moduli spaces of smooth and stable curves, focusing in particular on low degree cohomology. We also give a new proof of Harer's theorem describing the…

We introduce and analyze a new geometric structure on topological surfaces generalizing the complex structure. To define this so called higher complex structure we use the punctual Hilbert scheme of the plane. The moduli space of higher…

We survey recent work on moduli spaces of manifolds with an emphasis on the role played by (stable and unstable) homotopy theory. The theory is illustrated with several worked examples.