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Orbifolds in Mathematics and Physics
Edited by: Alejandro Adem, University of Wisconsin, Madison, WI, Jack Morava, Johns Hopkins University, Baltimore, MD, and Yongbin Ruan, University of Wisconsin, Madison, WI
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Contemporary Mathematics
2002; 358 pp; softcover
Volume: 310
ISBN-10: 0-8218-2990-4
ISBN-13: 978-0-8218-2990-5
List Price: US$103
Member Price: US$82.40
Order Code: CONM/310
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This book 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 current 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 recent 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. By presenting the work of a broad range of mathematicians and physicists who use and study orbifolds, it familiarizes readers with the various points of view and types of results the researchers bring to the subject.

Readership

Advanced graduate students and researchers interested in orbifolds or in connections between mathematical subject areas

Table of Contents

  • D. Abramovich, T. Graber, and A. Vistoli -- Algebraic orbifold quantum products
  • W. Chen and Y. Ruan -- Orbifold Gromov-Witten theory
  • C. Dong, K. Liu, and X. Ma -- On orbifold elliptic genus
  • T. Graber and E. Zaslow -- Open-string Gromov-Witten invariants: Calculations and a mirror "theorem"
  • T. J. Jarvis and T. Kimura -- Orbifold quantum cohomology of the classifying space of a finite group
  • R. M. Kaufmann -- Orbifold Frobenius algebras, cobordisms and monodromies
  • E. Lupercio and B. Uribe -- Loop groupoids, Gerbes, and twisted sectors on orbifolds
  • M. Mariño and C. Vafa -- Framed knots at large \(N\)
  • I. Moerdijk -- Orbifolds as groupoids: An introduction
  • M. Poddar -- Orbifold cohomology group of toric varieties
  • Z. Qin and W. Wang -- Hilbert schemes and symmetric products: A dictionary
  • Y. Ruan -- Stringy orbifolds
  • E. Sharpe -- Discrete torsion, quotient stacks, and string orbifolds
  • K. Wendland -- Orbifold constructions of \(K3\): A link between conformal field theory and geometry
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