## Orbifolds in Mathematics and Physics: Proceedings of a Conference on Mathematical Aspects of Orbifold String Theory, May 4-8, 2001, University of Wisconsin, Madison, WisconsinThis volume publishes papers originally presented at a conference on the Mathematical Aspects of Orbifold String Theory, hosted by the University of Wisconsin-Madison. It contains a great deal of information not fully covered in the published literature and showcases the state of the art in orbital string theory. The subject of orbifolds has a long prehistory, going back to the work of Thurston and Haefliger, with roots in the theory of manifolds, group actions, and foliations. The explosion of activity on the topic has been powered by applications of orbifolds to moduli problems and quantum field theory. The present volume presents an interdisciplinary look at orbifold problems. Topics such as stacks, vertex operator algebras, branes, groupoids, K-theory and quantum cohomology are discussed. The book reflects the thinking of distinguished investigators working in the areas of mathematical physics, algebraic geometry, algebraic topology, symplectic geometry and representation theory. |

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### Contents

1 | |

Orbifold GromovWitten theory | 25 |

On orbifold elliptic genus | 87 |

Calculations and a mirror theorem | 107 |

Orbifold quantum cohomology of the classifying space of a finite group | 123 |

Orbifold Frobenius algebras cobordisms and monodromies | 135 |

Loop groupoids gerbes and twisted sectors on orbifolds | 163 |

Framed knots at large N | 185 |

An introduction | 205 |

Orbifold cohomology group of toric varieties | 223 |

A dictionary | 233 |

Stringy orbifolds | 259 |

Discrete torsion quotient stacks and string orbifolds | 301 |

A link between conformal field theory and geometry | 333 |

### Other editions - View all

Orbifolds in Mathematics and Physics: Proceedings of a Conference on ... Alejandro Adem,Jack Morava,Yongbin Ruan No preview available - 2002 |

### Common terms and phrases

arrow automorphism Calabi-Yau canonical Chern class of compatible cohomology ring compatible systems complex component conjugacy class connected construction corresponding curve define definition denote describe strings discrete torsion divisor element equation equivariant étale groupoid fiber field finite group Frobenius algebra function G-action gauge geodesic geometry gerbe given Gromov–Witten invariants group actions groupoid G Heisenberg algebra Hilbert schemes homomorphism induced injection integral isomorphism class K-theory Kuranishi Lemma line bundle linear manifold map f marked points Math Mathematics metric mirror symmetry moduli space Morita equivalent morphism neighborhood nodal orbifold bundle orbifold CFTs orbifold cohomology orbifold structure proof Proposition pseudo-holomorphic map pull-back quantum cohomology quotient stacks Riemann surface Ruan SCFTs sigma model singular smooth stable maps string orbifolds string theory Theorem topological trivial twisted sectors uniformizing system Vafa vector bundle