相关论文: Systematic approach to cyclic orbifolds

We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string…

The CW structure of certain spaces, such as effective orbifolds, can be too complicated for computational purposes. In this paper we use the concept of $\mathbf{q}$-CW complex structure on an orbifold, to detect torsion in its integral…

Motivated by orbifold string theory, we introduce orbifold cohomology group for any almost complex orbifold and orbifold Dolbeault cohomology for any complex orbifold. Then, we show that our new cohomology group satisfies Poincare duality…

We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…

Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries are investigated.

Orbifolds of two-dimensional quantum field theories have a natural formulation in terms of defects or domain walls. This perspective allows for a rich generalisation of the orbifolding procedure, which we study in detail for the case of…

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

A general theory of permutation orbifolds is developed for arbitrary twist groups. Explicit expressions for the number of primaries, the partition function, the genus one characters, the matrix elements of modular transformations and for…

We prove that the underlying set of an orbifold equipped with the ring of smooth real-valued functions completely determines the orbifold atlas. Consequently, we obtain an essentially injective functor from orbifolds to differential spaces.

This text introduces geometric quantization on orbifolds. After reviewing the necessary background, it develops new treatments of prequantization, polarizations, and metaplectic correction for symplectic orbifolds.

We present a general deconstruction procedure aimed at recognizing whether a given conformal model may be obtained as an orbifold of another one, and to identify the twist group and the original model in terms of some readily available…

A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…

In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…

The theory of twistors on foliated manifolds is developed and the twistor space of the normal bundle is constructed. It is demonstrated that the classical constructions of the twistor theory lead to foliated objects and permit to formulate…

Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…

There is a classical geometric construction which uses a binary quadratic form to define an involution on the space of binary d-ics. We give a complete characterization of a general class of such involutions which are definable using…

This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.

In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…

We have found a "non-purely-constructive" method of acquiring algebraic cycles involving multiple steps. This note tries to present the main idea in the last step by concentrating on an example of 4-folds. The method demonstrates a contrast…