**Contemporary Mathematics**

Volume: 310;
2002;
358 pp;
Softcover

MSC: Primary 81; 55; 17; 19;

Print ISBN: 978-0-8218-2990-5

Product Code: CONM/310

List Price: $105.00

Individual Member Price: $84.00

**Electronic ISBN: 978-0-8218-7900-9
Product Code: CONM/310.E**

List Price: $105.00

Individual Member Price: $84.00

# Orbifolds in Mathematics and Physics

Share this page *Edited by *
*Alejandro Adem; Jack Morava; Yongbin Ruan*

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.

#### Table of Contents

# Table of Contents

## Orbifolds in Mathematics and Physics

- Contents v6 free
- Preface vii8 free
- Algebraic orbifold quantum products 110 free
- Orbifold Gromov-Witten theory 2534
- On orbifold elliptic genus 8796
- Open-string Gromov-Witten invariants: Calculations and a mirror "theorem" 107116
- Orbifold quantum cohomology of the classifying space of a finite group 123132
- Orbifold Frobenius algebras, cobordisms, and monodromies 135144
- Loop groupoids, gerbes, and twisted sectors on orbifolds 163172
- Framed knots at large N 185194
- Orbifolds as groupoids: An introduction 205214
- Orbifold cohomology group of toric varieties 223232
- Hilbert schemes and symmetric products: A dictionary 233242
- 1. Introduction 233242
- 2. The cohomology ring of Hilbert schemes 237246
- 3. The orbifold cohomology ring of symmetric products I 240249
- 4. The orbifold cohomology ring of symmetric products II 247256
- 5. The deformed orbifold cohomology ring of symmetric products 252261
- 6. Open questions 255264
- References 256265

- Stringy orbifolds 259268
- Discrete torsion, quotient stacks, and string orbifolds 301310
- Orbifold constructions of K3: A link between conformal field theory and geometry 333342

#### Readership

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