Related papers: From Torus Bundles to Particle-Hole Equivariantiza…

We extend work of Davis and Januszkiewicz by considering {\it omnioriented} toric manifolds, whose canonical codimension-2 submanifolds are independently oriented. We show that each omniorientation induces a canonical stably complex…

Continuing our previous work on graded twisting of Hopf algebras and monoidal categories, we introduce a graded twisting construction for equivariant comodule algebras and module categories. As an example we study actions of quantum…

We introduce a pre-symplectic structure on the space of connections in a G-principal bundle over a four-manifold and a Hamiltonian action on it of the group of gauge transformations that are trivial on the boundary. The moment map is given…

We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second…

By work of Kirby-Siebenmann \cite{KirbySiebenmann} and Kervaire-Milnor \cite{KervaireMilnor}, there are only finitely many smooth manifolds homeomorphic to a given closed topological manifold. A construction involving Whitehead torsion…

This is the second paper in a series on enumerative invariants counting self-dual objects in self-dual categories, and is a sequal to (arXiv:2302.00038). Ordinary enumerative invariants in abelian categories can be seen as invariants for…

On a symplectic manifold $M$, the quantum product defines a complex, one parameter family of flat connections called the A-model or Dubrovin connections. Let $\hbar$ denote the parameter. Associated to them is the quantum $\mathcal{D}$ -…

We study complex Chern-Simons theory on a Seifert manifold $M_3$ by embedding it into string theory. We show that complex Chern-Simons theory on $M_3$ is equivalent to a topologically twisted supersymmetric theory and its partition function…

Let $X$ be the wonderful compactification of a complex adjoint symmetric space $G/K$ such that $rk(G/K)=rk(G)-rk(K)$. We show how to extend equivariant vector bundles on $G/K$ to equivariant vector bundles on $X$, generated by their global…

Let X be a smooth projective variety with the action of the n dimensional torus. The article describes the moduli space of torus equivariant morphisms from stable toric varieties into X as the inverse limit of the GIT quotients of X and…

This paper is a sequel to "Localization of $\frak{u}$-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type)…

A covariant functor from the category of mapping tori to a category of AF-algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding AF-algebras. We use this functor…

We define parametrized cobordism categories and study their formal properties as bivariant theories. Bivariant transformations to a strongly excisive bivariant theory give rise to characteristic classes of smooth bundles with strong…

In this paper we outline a recent construction of a Chern-Weil isomorphism for the equivariant Brauer group of $\mathbb R^n$ actions on a principal torus bundle, where the target for this isomorphism is a "dimensionally reduced" \vCech…

Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum sl(2) were obtained by the last three authors in [arXiv:1404.7289]. In their construction the quantum parameter $q$ is a root of unity of order…

We study the existence of $S^1$-equivariant characteristic classes on certain natural infinite rank bundles over the loop space $LM$ of a manifold $M$. We discuss the different $S^1$-equivariant cohomology theories in the literature and…

In dimension 4, we extend the correspondence between compact nonsingular toric varieties and regular fans to a correspondence between almost complex torus manifolds and families of multi-fans in a geometric way, where an (almost) complex…

We analyse the classical moduli spaces of supersymmetric vacua of 3d N=2 Chern-Simons quiver gauge theories. We show quite generally that the moduli space of the 3d theory always contains a baryonic branch of a parent 4d N=1 quiver gauge…

Massless modes of both heterotic and Type II string compactifications on compact manifolds are determined by vector bundle valued cohomology classes. Various applications of our recent algorithm for the computation of line bundle valued…

J. Pevtsova and the author constructed a ``universal $p$-nilpotent operator" for an infinitesimal group scheme $G$ over a field $k$ of characteristic $p > 0$ which led to coherent sheaves on the scheme of 1-parameter subgroups of $G$…