Related papers: On characteristic classes of Q-manifolds

We introduce the quantum isomeric supercategory and the quantum affine isomeric supercategory. These diagrammatically defined supercategories, which can be viewed as isomeric analogues of the HOMFLYPT skein category and its affinization,…

The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…

Characteristic classes of oriented vector bundles can be identified with cohomology classes of the disjoint union of classifying spaces BSO_n of special orthogonal groups SO_n with n=0,1,... A characteristic class is stable if it extends to…

We compute quantum character varieties of arbitrary closed surfaces with boundaries and marked points. These are categorical invariants $\int_S\mathcal A$ of a surface $S$, determined by the choice of a braided tensor category $\mathcal A$,…

We classify those manifolds of positive euler characteristic on which a lie group G acts with cohomogeneity one, where G is classical simple

We construct characteristic classes of 4-manifold bundles using $SO(3)$-Yang-Mills theory and Seiberg-Witten theory for families.

We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

In this paper, we define in an intrinsic way operators on a compact Lie group by means of symbols using the representations of the group. The main purpose is to show that these operators form a symbolic pseudo-differential calculus which…

One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. We provide explicit bounds on the primes appearing in the denominators of…

We introduce supergroup analogues of 3-manifold invariants $\hat{Z}$, also known as homological blocks, which were previously considered for ordinary compact semisimple Lie groups. We focus on superunitary groups, and work out the case of…

We classify open maximal subalgebras of all infinite-dimensional linearly compact simple Lie superalgebras. This is applied to the classification of infinite-dimensional Lie superalgebras of vector fields, acting transitively and…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such…

We consider complex manifolds that admit actions by holomorphic transformations of classical simple real Lie groups and classify all such manifolds in a natural situation. Under our assumptions, which require the group at hand to be…

In this paper we propose a new treatment about infinite dimensional manifolds, using the language of category and functor. Our definition of infinite dimensional manifolds is a natural generalization of finite dimensional manifolds in the…

We review Haefliger's differentiable cohomology for the pseudogroup of diffeomorphisms of $\mathbb{R}^q$. We investigate the structure needed to define such a cohomology, which, remarkably, is related to the so called Cartan distribution…

Consider a subgroup of finite index of modular group. We give an analytic criterion for a cuspidal divisor to be torsion in the Jacobian of the corresponding modular curve. By BelyI theorem, such a criterion would apply to any curve over a…

We introduce the notion of a super-representation of a quiver. For super-representations of quivers over a field of characteristic zero, we describe the corresponding (super)algebras of polynomial semi-invariants and polynomial invariants.

Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.