Two-Dimensional Orbifolds
نویسنده
چکیده
1 Definitions An orbifold is a Hausdorff space X0 along with an open cover {Ui} that is closed under finite intersection with the following properties. For each Ui there is an open set Ũi ⊆ R and a finite group Γi which acts on Ũi. In addition there is a homeomorphism φi : Ui ≈ Ũi/Γi and whenever Ui ⊂ Uj there is an injective homomorphism fij : Γi ↪→ Γj and Ũi can be embedded in Ũj such that the following diagram commutes. -
منابع مشابه
Spectral and Geometric Bounds on 2 - Orbifold Diffeomorphism
We show that a Laplace isospectral family of two dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that orbifolds of only finitely many orbifold diffeomorphism types may arise in any collection of 2-orbifolds satisfying lower bounds on sectional curvature and volume, ...
متن کاملClassification of 1D and 2D Orbifolds
We present a complete classification of all 1D and 2D orbifold compactifications. There exist 2 one-dimensional and 17 two-dimensional orbifolds. The classification includes orbifolds such as S/Z2 or T /Zn, as well as less familiar ones like T /Dn or the Möbius strip. We derive the explicit form of the basis functions and prove their orthonormality and completeness. Our study is based on the cl...
متن کاملEquivalence Classes of Boundary Conditions in SU(N) Gauge Theory on 2-dimensional Orbifolds
We study equivalence classes of boundary conditions in an SU(N) gauge theory on sixdimensional space-time including two-dimensional orbifold. For five kinds of two-dimensional orbifolds S/Z2 × S /Z2 and T /Zm (m = 2, 3, 4, 6), orbifold conditions and those gauge transformation properties are given and the equivalence relations among boundary conditions are derived. The classification of boundar...
متن کاملLectures on orbifolds and reflection groups
Orbifolds and the orbifold fundamental group are defined in Lecture 1. Lecture 2 deals with Euler characteristics of orbifolds and the classification of 2-dimensional orbifolds. the last three lectures concern orbifolds coming from groups genenerated by reflections (“reflectofolds”). MSC(2010): primary 57R18, 57S30.
متن کاملThe Chen-ruan Cohomology of Almost Contact Orbifolds
Comparing to the Chen-Ruan cohomology theory for the almost complex orbifolds, we study the orbifold cohomology theory for almost contact orbifolds. We define the Chen-Ruan cohomology group of any almost contact orbifold. Using the methods for almost complex orbifolds (see [2]), we define the obstruction bundle for any 3-multisector of the almost contact orbifolds and the Chen-Ruan cup product ...
متن کاملBrane Cube Realization of Three-dimensional Nonabelian Orbifolds
We study D-branes on three-dimensional orbifolds C/Γ where Γ are finite subgroups of SU(3). The quiver diagram of Zn × Zn ∈ SU(3) can be expressed in three-dimensional form. According to the correspondence between quiver diagrams and brane configurations, we construct a brane configuration for C/Zn×Zn which has essentially three-dimensional structrue. Brane configurations for nonabelian orbifol...
متن کامل