Related papers: Integral Lattices of the SU(2)-TQFT-Modules

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

It is given a canonical representation of prime ends in regular spatial domains and, on this basis, it is studied the boundary behavior of the so-called lower Q-homeomorphisms that are the natural generalization of the quasiconformal…

We describe the natural gluing map on sutured Floer homology which is induced by the inclusion of one sutured manifold (M',\Gamma') into a larger sutured manifold (M,\Gamma), together with a contact structure on M-M'. As an application of…

Let $F$ be a number field with ring of integers $\Oc_F$ and $\Dc$ a division $F$-algebra with a maximal cyclic subfield $K$. We study rings occurring as quotients of a natural $\Oc_F$-order $\Lambda$ in $\Dc$ by two-sided ideals. We reduce…

Foams are surfaces with branch lines at which three sheets merge. They have been used in the categorification of sl(3) quantum knot invariants and also in physics. The 2D-TQFT of surfaces, on the other hand, is classified by means of…

We hypothesize a new and more complete set of anomalies of certain quantum field theories (QFTs) and then give an eclectic verification. First, we propose a set of 't Hooft higher anomalies of 4d time-reversal symmetric pure…

An invariant for twisted K theory classes on a 3-manifold is introduced. The invariant is then applied to the twisted equivariant classes arising from the supersymmetric Wess-Zumino-Witten model based on the group SU(2). It is shown that…

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…

In this paper, we examine Atiyah's Hermitian axiom for two-dimensional complex topological quantum field theories. Building on the correspondence between 2D TQFTs and Frobenius algebras, we find the algebraic objects corresponding to…

We derive an explicit formula for the Witten-Reshetikhin-Turaev SO(3)-invariants of lens spaces. We use the representation of the mapping class group of the torus corresponding to the Witten-Reshetikhin-Turaev SO(3)-TQFT to give such…

We study the quantization of a holomorphic two-form coupled to a Yang-Mills field on special manifolds in various dimensions, and we show that it yields twisted supersymmetric theories. The construction determines ATQFT's (Almost…

We consider 5d $\mathcal{N}=1$ SU(2) super Yang-Mills theory on $X\times S^1$, with $X$ a closed smooth four-manifold. A partial topological twisting along $X$ renders the theory formally independent of the metric on $X$. The theory depends…

We apply the mechanism of factorization homology to construct and compute category-valued two-dimensional topological field theories associated to braided tensor categories, generalizing the $(0,1,2)$-dimensional part of…

We study three natural bi-invariant partial orders on a certain covering group of the automorphism group of a bounded symmetric domain of tube type; these orderings are defined using the geometry of the Shilov boundary, Lie semigroup theory…

It is known that the 't Hooft anomalies of invertible global symmetries can be characterized by an invertible TQFT in one higher dimension. The analogous statement remains to be understood for non-invertible symmetries. In this note we…

This is the sequel to the author's previous paper which gives an extension of Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds. The main result of this paper asserts the following. Whenever the Seiberg-Witten invariants are defined…

We point out the existence of an arithmetical symmetry for the commutant of the modular matrices S and T. This symmetry holds for all affine simple Lie algebras at all levels and implies the equality of certain coefficients in any modular…

Almost integral TQFTs were introduced by Gilmer [Duke Math. J. 125 (2004) 389--413]. The aim of this paper is to modify the TQFT of the category of extended 3-cobordisms given by Turaev (in his book: Quantum invariants of knots and…

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…

We study manifolds arising as spaces of sections of complex manifolds fibering over the projective line with normal bundle of each section isomorphic to several copies of O(k). Such manifolds provide a natural setting for certain integrable…