This quantity is a suite of articles on orbifolds, algebraic curves with larger spin buildings, and comparable invariants of Gromov-Witten kind. Orbifold Gromov-Witten conception generalizes quantum cohomology for orbifolds, while spin cohomological box concept relies at the moduli areas of upper spin curves and is expounded via Witten's conjecture to the Gelfand-Dickey integrable hierarchies. a standard function of those very various having a look theories is the primary function performed by way of orbicurves in either one of them. Insights in a single concept can usually yield insights into the opposite. This booklet brings jointly for the 1st time papers relating to each side of this interplay. The articles within the assortment conceal varied subject matters, reminiscent of geometry and topology of orbifolds, cohomological box theories, orbifold Gromov-Witten idea, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of upper spin curves and spin cohomological box conception.
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