Related papers: Theta-functions on the Kodaira-Thurston manifold

In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…

In [4] and [5], we generalized the concept of completion of an infinitesimal group action $\zeta : {\mathfrak g} \to \mathfrak X (M)$ to an actual group action on a (non-compact) manifold $M$, originally introduced by R. Palais [9], and…

This paper examines the relationship between the symplectic quotient X//G of a Hamiltonian G-manifold X, and the associated symplectic quotient X//T, where T is a maximal torus, in the case in which X//G is a compact manifold or orbifold.…

We construct the functional integral of Abelian Chern-Simons theory with toral gauge group $\mathbb T=\mathfrak t/\Lambda \cong U(1)^n$ at level $K$, where $K:\Lambda\times\Lambda\to\mathbb Z$ is an even, integral, nondegenerate symmetric…

Let X be a complete toric variety of dimension n and \del the fan in a lattice N associated to X. For each cone \sigma of \del there corresponds an orbit closure V(\sigma) of the action of complex torus on X. The homology classes…

In this paper, we study the Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds. These zeta functions are defined on one complex variable $s$ in some right half-plane of $\mathbb{C}$. We use the Selberg trace…

We discuss how the global geometry and topology of manifolds depend on different group actions of their fundamental groups, and in particular, how properties of a non-trivial compact 4-dimensional cobordism $M$ whose interior has a complete…

Several sets of quaternionic functions are described and studied with respect to hy-perholomorphy, addition and (non commutative) multiplication, on open sets of H, then Hamil-ton 4-manifolds analogous to Riemann surfaces, for H instead of…

The Wirtinger integral is one of the integral representations of the Gauss hypergeometric function. Its integrand is given by a product of complex powers of theta functions. We study the structure of the twisted homology and cohomology…

Let $(M, g, \omega, f, \lambda)$ be a K\"{a}hler gradient Ricci soliton in real dimension four. One first observes that it is an integrable Hamiltonian system in a classical sense. Indeed, all known complete examples are toric and the…

Let $M$ be a finite volume analytic pseudo-Riemannian manifold that admits an isometric $G$-action with a dense orbit, where $G$ is a connected non-compact simple Lie group. For low-dimensional $M$, i.e. $\dim(M) < 2\dim(G)$, when the…

We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary,…

We lay down a general framework for how to construct a Topological Quantum Field Theory $Z_A$ defined on shaped triangulations of orientable 3-manifolds from any Pontryagin self-dual locally compact abelian group $A$. The partition function…

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

The real Fourier-Mukai transform sends a section of a torus fibration to a connection over the total space of the dual torus fibration. By this method, Leung, Yau and Zaslow introduced deformed Hermitian Yang-Mills (dHYM) connections for…

The Theta invariant is the simplest 3-manifold invariant defined with configuration space integrals. It is actually an invariant of rational homology spheres equipped with a combing over the complement of a point. It can be computed as the…

This paper outlines an approach to the non-abelian theta functions of the $SU(2)$-Chern-Simons theory with the methods used by A. Weil for studying classical theta functions. First we translate in knot theoretic language classical theta…

Using the $u$-plane integral as a tool, we derive a formula for the partition function of the simplest nontrivial (topologically twisted) Argyres-Douglas theory on compact, oriented, simply connected, four-manifolds without boundary and…

Infinitesimal symmetries of a classical mechanical system are usually described by a Lie algebra acting on the phase space, preserving the Poisson brackets. We propose that a quantum analogue is the action of a Lie bi-algebra on the…

We introduce a new 2-parameter family of sigma models exhibiting Poisson-Lie T-duality on a quasitriangular Poisson-Lie group $G$. The models contain previously known models as well as a new 1-parameter line of models having the novel…