This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies. A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.
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978-0-8218-3534-0 (9780821835340)
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Schweitzer Klassifikation
Moduli spaces of curves with effective $r$-spin structures by A. Polishchuk A construction of Witten's top Chern class in $K$-theory by A. Chiodo Witten's conjecture and the Virasoro conjecture for genus up to two by Y.-P. Lee Idempotents on the big phase space by X. Liu Singularities with symmetries, orbifold Frobenius algebras and mirror symmetry by R. M. Kaufmann The cohomology ring of crepant resolutions of orbifolds by Y. Ruan Differential characters on orbifolds and string connections I: Global quotients by E. Lupercio and B. Uribe HKR characters and higher twisted sectors by J. Morava Combinatorics of binomial decompositions of the simplest Hodge integrals by S. V. Shadrin The orbifold cohomology of the moduli of genus-two curves by J. Spencer.
