Related papers: The AG-invariant for (m+2)-angulations
In our previous publications we have introduced a differential calculus on the algebra $U(gl(m))$ based on a new form of the Leibniz rule which differs from that usually employed in Noncommutative Geometry. This differential calculus…
In This paper, we survey recent progress on the theory of Gromov- Witten invariants on Hilbert schemes of points mainly on elliptic surfaces and simply connected minimal surface of general type. In particular, we focus on the aspects of…
Meier and Zupan showed that every surface in the four-sphere admits a bridge trisection and can therefore be represented by three simple tangles. This raises the possibility of applying methods from link homology to knotted surfaces. We use…
We propose a way of computing 4-manifold invariants, old and new, as chiral correlation functions in half-twisted 2d $\mathcal{N}=(0,2)$ theories that arise from compactification of fivebranes. Such formulation gives a new interpretation of…
It is proved that a multiset of permissible arcs over a tiling is uniquely determined by its intersection vector under a mild condition. This generalizes a classical result over marked surfaces with triangulations. We apply this result to…
The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame…
We introduce a diffeomorphism invariant of $4$-manifolds, the $\mathrm{Pin}^-(2)$-monopole invariant, defined by using the $\mathrm{Pin}^-(2)$-monopole equations. We compute the invariants of several $4$-manifolds, and prove gluing…
This paper begins a new approach to the $r$-trace formula, without removing the nontempered contribution to the spectral side. We first establish an invariant trace formula whose discrete spectral terms are weighted by automorphic…
The centers of the generic central simple algebras with involution are interesting objects in the theory of central simple algebras. These fields also arise as invariant fields for linear actions of projective orthogonal or symplectic…
In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain…
In [LP] the authors defined symplectic "Local Gromov-Witten invariants" associated to spin curves and showed that the GW invariants of a Kahler surface X with p_g>0 are a sum of such local GW invariants. This paper describes how the local…
We present a method of computing genus zero two-point descendant Gromov-Witten invariants via one-point invariants. We apply our method to recover some of calculations of Zinger and Popa-Zinger, as well as to obtain new calculations of…
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF, Chern-Simons and 2-dimensional…
We present an algorithmic framework for computing generators for the ring of invariants of an Artin-Schreier curve. We give explicit invariants for almost all Artin-Schreier curves of genus up to~8 in standard form, and for a handful of…
We prove new local inequality for divisors on surfaces and utilize it to compute $\alpha$-invariants of singular del Pezzo surfaces, which implies that del Pezzo surfaces of degree one whose singular points are of type $\mathbb{A}_{1}$,…
This paper considers gauge-invariant and covariant gravitational perturbations on arbitrary vacuum locally rotationally symmetric (LRS) class II space-times. Ultimately, we derive four decoupled equations governing four specific…
We discuss the detectable subspaces of an operator. We analyse the relation between the M-function (the abstract Dirichlet to Neumann map) and the resolvent bordered by projections onto the detectable subspaces. The abstract results are…
We describe the J-invariant of a semi-simple algebraic group G over a generic splitting field of a Tits algebra of G in terms of the J-invariant over a base field.
In [1,2] we established and discussed the algebra of observables for $2+1$ gravity at both the classical and quantum level, and gave a systematic discussion of the reduction of the expected number of independent observables to $6g - 6 (g >…
In this article we describe indecomposable objects of the derived categories of a branch class of associative algebras. To this class belong such known classes of algebras as gentle algebras, skew-gentle algebras and certain degenerations…