Related papers: Comments on the classification of orientifolds
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…
Examples of nonformal simply connected symplectic manifolds are constructed.
It is shown that every orthogonal terrain, i.e., an orthogonal (right-angled) polyhedron based on a rectangle that meets every vertical line in a segment, has a grid unfolding: its surface may be unfolded to a single non-overlapping piece…
We outline a relationship between conformal field theories and spectral problems of ordinary differential equations, and discuss its generalisation to models related to classical Lie algebras.
We prove that the set of orthogonal separable coordinates on an arbitrary (pseudo-)Riemannian manifold carries a natural structure of a projective variety, equipped with an action of the isometry group. This leads us to propose a new,…
The main properties of indefinite Kac-Moody and Borcherds algebras, considered in a unified way as Lorentzian algebras, are reviewed. The connection with the conformal field theory of the vertex operator construction is discussed. By the…
We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…
The concept of orbifolds should unify differential geometry with equivariant homotopy theory, so that orbifold cohomology should unify differential cohomology with proper equivariant cohomology theory. Despite the prominent role that…
A classification of stable singular points on world sheets of open relativistic strings is carried out.
We investigate the geometry of codimension one foliations on smooth projective varieties defined over fields of positive characteristic with an eye toward applications to the structure of codimension one holomorphic foliations on projective…
It is formally constructed a normal form for a class of real-formal surfaces defined near a CR Singularity.
We give an exposition on the current status of classification of operator algebraic conformal field theories. We explain roles of complete rationality and alpha-induction for nets of subfactors in such a classification and present the…
This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of…
Conformal fields are a recently discovered class of representations of the algebra of vector fields in $N$ dimensions. Invariant first-order differential operators (exterior derivatives) for conformal fields are constructed.
The parameter-space orbifold construction of open and unoriented toroidal and (target-space) orbifold compactifications is briefly reviewed, with emphasis on the underlying geometrical framework. A class of chiral four-dimensional type-I…
We present here definitions and constructions basic for the theory of monoidal and tensor categories. We provide references to the original sources, whenever possible. Group-theoretical categories are used as examples
We introduce a construction of oriented matroids from a triangulation of a product of two simplices. For this, we use the structure of such a triangulation in terms of polyhedral matching fields. The oriented matroid is composed of…
There are a least uncountably many diffeomorphism types for open manifolds. Hence the classification problem is extremely difficult. We proceed as follows: We define several uniform structures of proper metric spaces and consider their arc…
The free field representation of the osp(1|2) current algebra is analyzed. The four point conformal blocks of the theory are studied. The structure constants for the product of an arbitrary primary operator and a primary field that…
We develop a general theory of 3-dimensional ``orbifold completion'', to describe (generalised) orbifolds of topological quantum field theories as well as all their defects. Given a semistrict 3-category $\mathcal{T}$ with adjoints for all…