### Abstract

Ideas from deformation quantization applied to algebra with one generator lead to the construction of non-linear flat connection, whose parallel sections have algebraic significance. The moduli space of parallel sections is studied as an example of bundle-like objects with discordant (sogo) transition functions, which suggests a method to treat families of meromorphic functions with smoothly varying branch points.

Original language | English |
---|---|

Title of host publication | Progress in Mathematics |

Publisher | Springer Basel |

Pages | 303-324 |

Number of pages | 22 |

DOIs | |

Publication status | Published - 2007 Jan 1 |

### Publication series

Name | Progress in Mathematics |
---|---|

Volume | 252 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### Keywords

- Deformation quantization
- Gerbe
- Non-linear connections
- Star exponential functions

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology

## Fingerprint Dive into the research topics of 'Geometric objects in an approach to quantum geometry'. Together they form a unique fingerprint.

## Cite this

Omori, H., Maeda, Y., Miyazaki, N., & Yoshioka, A. (2007). Geometric objects in an approach to quantum geometry. In

*Progress in Mathematics*(pp. 303-324). (Progress in Mathematics; Vol. 252). Springer Basel. https://doi.org/10.1007/978-0-8176-4530-4_16