Related papers: Spin Modular Categories
In this paper we construct a family of cohomology classes on the moduli space of stable curves generalizing Witten's $r$-spin classes. They are parameterized by a phase space which has one extra dimension and in genus $0$ they correspond to…
We continue the program of constructing (pre)modular tensor categories from 3-manifolds first initiated by Cho-Gang-Kim using $M$ theory in physics and then mathematically studied by Cui-Qiu-Wang. An important structure involved is a…
Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…
In 2006 Habiro initiated a construction of generating functions for Witten-Reshetikhin-Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with Irmgard Buehler and Christian Blanchet we extended his…
Based on a pair of cohomology operations on so called $\delta-2$-formal spaces, we construct the integral cohomology rings of the classifying spaces of the Lie groups $Spin(n)$ and $Spin^{c}(n)$. As applications, we introduce characteristic…
Motivated by ideas from string theory and quantum field theory new invariants of knots and 3-dimensional manifolds have been constructed from complex algebraic structures such as Hopf algebras (Reshetikhin and Turaev), monoidal categories…
In this article, we will prove that the subsectors of $\alpha$-induced sectors for $M \rtimes \hat{G} \supset M$ forms a modular category, where $M \rtimes \hat{G}$ is the crossed product of $M$ by the group dual $\hat{G}$ of a finite group…
We use Gay and Kirby's description of 4-manifolds in terms of trisections and trisection diagrams to define a new 4-manifold invariant. The algebraic data are an indecomposable finite semisimple bimodule category over a pair of spherical…
We propose a systematic scheme for computing the variation of rearrangement operators arising in the recently developed spectral geometry on noncommutative tori and $\theta$-deformed Riemannian manifolds. It can be summarized as a category…
Arbitrarily many pairwise inequivalent modular categories can share the same modular data. We exhibit a family of examples that are module categories over twisted Drinfeld doubles of finite groups, and thus in particular integral modular…
By studying modular invariance properties of some characteristic forms, we obtain twisted anomaly cancellation formulas. We apply these twisted cancellation formulas to study divisibilities on spin manifolds and congruences on spin$^c$…
We show that the Reshetikhin-Turaev-Walker invariant of 3-manifolds can be normalized to obtain an invariant of 4-dimensional thickenings of 2-complexes. Moreover when the underlying semisimple tortile category comes from the…
We study the classification of submodules of module categories over monoidal categories, extending ideas of Coulembier on the classification of tensor ideals in monoidal categories. We develop a framework that applies to module categories…
We identify a class of "semi-modular" forms invariant on special subgroups of $GL_2(\mathbb Z)$, which includes classical modular forms together with complementary classes of functions that are also nice in a specific sense. We define an…
We introduce the notion of mutation of $n$-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules…
Cubic complexes appear in the theory of finite type invariants so often that one can ascribe them to basic notions of the theory. In this paper we begin the exposition of finite type invariants from the `cubic' point of view. Finite type…
In this paper we study irreducible tensor products of representations of alternating groups in characteristics 2 and 3. In characteristic 3 we completely classify irreducible tensor products, while in characteristic 2 we completely classify…
In this paper we define a class of state-sum invariants of compact closed oriented piece-wise linear 4-manifolds using finite groups. The definition of these state-sums follows from the general abstract construction of 4-manifold invariants…
This work reports on joint research with Manuel Saorin. For an algebra A over an algebraically closed field k the set of A-module structures on k d forms an affine algebraic variety. The general linear group Gl d (k) acts on this variety…
We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…