Related papers: Contact Dual Pairs
The canonical involution of a double (=iterated) tangent bundle may be dualized in different ways to yield relations between the Tulczyjew diffeomorphism, the Poisson anchor associated with the standard symplectic structure on the cotangent…
We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a…
Recently Baraglia showed how topological T-duality can be extended to apply not only to principal circle bundles, but also to non-principal circle bundles. We show that his results can also be recovered via two other methods: the…
We consider a Ziegler pair of plane arrangements, that is two plane arrangements $\mathcal{A}:f=0$ and $\mathcal{A}':f'=0$ in the projective space $\mathbb{P}^3$, such that the intersection lattices $L(\mathcal{A})$ and $L(\mathcal{A}')$…
We give rigorous foundations for parametrized homotopy theory in this monograph. After preliminaries on point-set topology, base change functors, and proper actions of non-compact Lie groups, we develop the homotopy theory of equivariant…
In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological…
We study Jacobi structures on the dual bundle $A^\ast$ to a vector bundle $A$ such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We…
We continue the study of linear families of contact forms on 3-manifolds begun in our paper `Contact geometry and complex surfaces'. The present paper introduces Teichmuller and moduli spaces for so-called taut contact circles. By…
A new geometric framework is developed to describe non-conservative classical field theories, which is based on multisymplectic and contact geometries. Assuming certain additional conditions and using the forms that define this multicontact…
Properties of metrics and pairs consisting of left and right connections are studied on the bimodules of differential 1-forms. Those bimodules are obtained from the derivation based calculus of an algebra of matrix valued functions, and an…
We outline in detail the general caloron correspondence for the group of automorphisms of an arbitrary principal $G$-bundle $Q$ over a manifold $X$, including the case of the gauge group of $Q$. These results are used to define…
We present a new construction of codimension-one foliations from pairs of contact structures in dimension three. This constitutes a converse result to a celebrated theorem of Eliashberg and Thurston on approximations of foliations by…
We observe, utilize dualities in differential equations and differential inequalities, dualities between comparison theorems in differential equations, and obtain dualities in "swapping" comparison theorems in differential equations. These…
Since the 1974 paper by Peskine and Szpiro, liaison theory via complete intersections, and more generally via Gorenstein varieties, has become a standard tool kit in commutative algebra and algebraic geometry, allowing to compare algebraic…
The Heisenberg double of a Hopf algebra may be regarded as a quantum analogue of the cotangent bundle of a Lie group. Quantum duality principle describes relations between a Hopf algebra, its dual, and their Heisenberg double in a way which…
The subject of this paper is a Jacobian, introduced by F. Lazzeri, (unpublished), associated to every compact oriented riemannian manifold of dimension twice an odd number. We start the investigation of Torelli type problems and Schottky…
We extend the Horrocks correspondence between vector bundles and cohomology modules on the projective plane to the product of two projective lines. We introduce a set of invariants for a vector bundle on the product of two projective lines,…
We propose to study homomorphisms of connectome graphs. Homomorphisms can be studied as sequences of elementary homomorphisms - folds, which identify pairs of vertices. Several fold types are defined. Initial computation results for some…
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of…
In this paper we continue the study (initiated in a previous article) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general…