相关论文: Algebraic topology and modular forms

Topological recursion associates to a spectral curve, a sequence of meromorphic differential forms. A tangent space to the "moduli space" of spectral curves (its space of deformations) is locally described by meromorphic 1-forms, and we use…

The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…

In this paper we present rigorously and as succintly as possible the theory of elliptic quasi-modular forms by means of moduli spaces and the Gauss-Manin connection, and deal with one of the main historical appearances of quasi-modular…

We relate analytically defined deformations of modular curves and modular forms from the literature to motivic periods via cohomological descriptions of deformation theory. Leveraging cohomological vanishing results, we prove the existence…

In this paper, we consider coalgebra measurings and the maps induced by them between Hochschild and cyclic homology of algebras. We show that these induced maps are well behaved with respect to the various structures appearing on Hochschild…

This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In a previous paper, we introduce the notion of formal manifolds and develop the…

We show that mapping class groups associated to all types of real algebraic curves are virtual duality groups. We also deduce some results about the orbifold homotopy groups of the moduli spaces of real algebraic curves. We achieve these…

Aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which controls deformations of Hom-Leibniz algebra structure. The cohomology and the associated deformation theory for Hom-Leibniz algebras as…

We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic…

We continue the study of linear families of contact forms on 3-manifolds begun in our paper `Contact geometry and complex surfaces'. The present paper introduces Teichmuller and moduli spaces for so-called taut contact circles. By…

The algebraic notion of a pivotal module category was developed by Schaumann and Shimizu and is central to the description of boundary conditions in conformal field theory according to a proposal by Fuchs and Schweigert. In this paper, we…

Recent work on homotopy type theory exploits an exciting new correspondence between Martin-Lof's dependent type theory and the mathematical disciplines of category theory and homotopy theory. The category theory and homotopy theory suggest…

We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a "determinant" map from this moduli surface to (Z/NZ)*; its fibers are the components of the…

We explore various formality and finiteness properties in the differential graded algebra models for the Sullivan algebra of piecewise polynomial rational forms on a space. The 1-formality property of the space may be reinterpreted in terms…

This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis, their properties depend on…

Motivated by the work of Cappell, Deturck, Gluch and Miller, we extend the notion of cohomology of harmonic forms (of a compact manifold with boundary) to the abstract setting of Hilbert complexes. Then, we present some geometric…

We define new higher-order Alexander modules $\mathcal{A}_n(C)$ and higher-order degrees $\delta_n(C)$ which are invariants of the algebraic planar curve $C$. These come from analyzing the module structure of the homology of certain…

In the context of orientable circuits and subcomplexes of these as representing certain singular spaces, we consider characteristic class formulas generalizing those classical results as seen for the Riemann-Hurwitz formula for regulating…