Contents Preface vii Algebraic orbifold quantum products DAN ABRAMOVICH, TOM GRABER, AND ANGELO VISTOLI 1 Orbifold Gromov-Witten theory WEIMIN CHEN AND YONGBIN RUAN 25 On orbifold elliptic genus CHONGYING DONG, KEFENG LIU, AND XIAONAN MA 87 Open-string Gromov-Witten invariants: Calculations and a mirror "theorem" TOM GRABER AND ERIC ZASLOW 107 Orbifold quantum cohomology of the classifying space of a finite group TYLER J. JARVIS AND TAKASHI KIMURA 123 Orbifold Frobenius algebras, cobordisms, and monodromies RALPH M. KAUFMANN 135 Loop groupoids, gerbes, and twisted sectors on orbifolds ERNESTO LUPERCIO AND BERNARDO URIBE 163 Framed knots at large N MARCOS MARINO AND CUMRUN VAFA 185 Orbifolds as groupoids: An introduction IEKE MOERDIJK 205 Orbifold cohomology group of toric varieties MAINAK PODDAR 223 Hilbert schemes and symmetric products: A dictionary ZHENBO QIN AND WEIQIANG WANG 233 Stringy orbifolds YONGBIN RUAN 259 Discrete torsion, quotient stacks, and string orbifolds ERIC SHARPE 301 v
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