相关论文: Integral Lattices in TQFT

We study Quot schemes of vector bundles on algebraic curves. Marian and Oprea gave a description of a topological quantum field theory (TQFT) studied by Witten in terms of intersection numbers on Quot schemes of trivial bundles. Since these…

First some old as well as new results about P.I. algebras, Ore extensions, and degrees are presented. Then quantized $n\times r$ matrices as well as quantized factor algebras of $M_q(n)$ are analyzed. The latter are the quantized function…

Certain vertex operator algebras have integral forms (integral spans of bases which are closed under the countable set of products). It is unclear when they (or integral multiples of them) are integral as lattices under the natural bilinear…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…

An example of a finite dimensional factorizable ribbon Hopf C-algebra is given by a quotient H=u_q(g) of the quantized universal enveloping algebra U_q(g) at a root of unity q of odd degree. The mapping class group M_{g,1} of a surface of…

Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…

A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI…

We prove several fundamental results about divisorial integral domains in the setup of multiplicative lattices.

We study real and integral structures in the space of solutions to the quantum differential equations. First we show that, under mild conditions, any real structure in orbifold quantum cohomology yields a pure and polarized tt^*-geometry…

Euclidean lattices occupy a central position in number theory, the geometry of numbers, and modern cryptography. In the present article, the theory of Euclidean lattices is employed to investigate normed $\mathbb{Z}$-modules of finite rank.…

Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems.…

We introduce the concept of a quantum background and a functor QFT. In the case that the QFT moduli space is smooth formal, we construct a flat quantum superconnection on a bundle over QFT which defines algebraic structures relevant to…

Let $d$ be a square free positive integer and $\mathbb{Q}(\sqrt{d})$ a totally real quadratic field over $\mathbb{Q}$. We show there exists an arithmetic lattice L in $SL(8,\mathbb{R})$ with entries in the ring of integers of…

We construct new special Lagrangian submanifolds in complex Euclidean space using a pair of minimal Legendrian submanifolds in odd-dimensional spheres and certain Lagrangian surface belonging to a family that can be considered as a…

In this paper, we use a topological quantum field theory (TQFT) to define families of new homology theories of a $2$-dimensional CW complex of a smooth closed surface. The dimensions of these homology groups can be used to count the number…

This paper deals with lattices $(L,\Vert~\Vert)$ over polynomial rings, where $L$ is a finitely generated module over $k[t]$, the polynomial ring over the field $k$ in the indeterminate $t$, and $\Vert~\Vert$ is a discrete real-valued…

We propose new tools based on basic lattice theory to calculate the integral cohomology of the quotient of a manifold by an automorphism group of prime order. As examples of applications, we provide the Beauville--Bogomolov forms of some…

In the paper is we generalize known descriptions of rings of semi-invariants for regular modules over Euclidean and canonical algebras to arbitrary concealed-canonical algebras.

We construct families of TQFT's over the finite field Z/pZ starting from an integral TQFT obtained by Frohman and Nicas. These TQFT's are likely to describe the constant order contributions of the cyclotomic integer expansions of the…

We define and study a natural system of tautological rings on the moduli spaces of marked curves at the level of differential forms. We show that certain 2-forms obtained from the natural normal functions on these moduli spaces are…