**Contemporary Mathematics**

Volume: 403;
2006;
189 pp;
Softcover

MSC: Primary 14; 53;

Print ISBN: 978-0-8218-3534-0

Product Code: CONM/403

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

**Electronic ISBN: 978-0-8218-7993-1
Product Code: CONM/403.E**

List Price: $65.00

AMS Member Price: $52.00

MAA Member Price: $58.50

# Gromov-Witten Theory of Spin Curves and Orbifolds

Share this page *Edited by *
*Tyler J. Jarvis; Takashi Kimura; Arkady Vaintrob*

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.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry, topology, and mathematical physics.

# Table of Contents

## Gromov-Witten Theory of Spin Curves and Orbifolds

- Contents v6 free
- Introduction vii8 free
- Moduli Spaces of Curves with Effective r-Spin Structures 110 free
- A Construction of Witten's Top Chern Class in K-Theory 2130
- Witten's Conjecture and the Virasoro Conjecture for Genus up to Two 3140
- ldempotents on the Big Phase Space 4352
- Singularities with Symmetries, Orbifold Frobenius Algebras and Mirror Symmetry 6776
- The Cohomology Ring of Crepant Resolutions of Orbifolds 117126
- Differential Characters on Orbifolds and String Connections I: Global Quotients 127136
- HKR characters and higher twisted sectors 143152
- Combinatorics of Binomial Decompositions of the Simplest Hodge Integrals 153162
- The Orbifold Cohomology of the Moduli of Genus-Two Curves 167176
- List of Participants and Abstracts 185194