This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role in recent mathematical advances. For example, algebraic versions of higher homotopies have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations and deformation philosophy, a basic observation is that higher homotopy structures behave much better than strict structures.

*Higher structures in geometry and physics. In Honor of Murray Gerstenhaber and Jim Stasheff.* Edited by: Cattaneo, A S; Giaquinto, A; Xu, P (2011). Boston: Birkhäuser.

## Abstract

This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. The ideas of higher homotopies and algebraic deformation have a growing number of theoretical applications and have played a prominent role in recent mathematical advances. For example, algebraic versions of higher homotopies have led eventually to the proof of the formality conjecture and the deformation quantization of Poisson manifolds. As observed in deformations and deformation philosophy, a basic observation is that higher homotopy structures behave much better than strict structures.

## Citations

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## Additional indexing

Item Type: | Edited Scientific Work |
---|---|

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 2011 |

Deposited On: | 23 Dec 2010 13:37 |

Last Modified: | 05 Apr 2016 14:29 |

Publisher: | Birkhäuser |

Series Name: | Progress in Mathematics |

Volume: | 287 |

Number of Pages: | 362 |

ISBN: | 978-0-8176-4734-6 |

Publisher DOI: | 10.1007/978-0-8176-4735-3 |

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