Progress in Mathematics

Higher Structures in Geometry and Physics

In Honor of Murray Gerstenhaber and Jim Stasheff

Editors: Cattaneo, Alberto S., Giaquinto, Anthony, Xu, Ping (Eds.)

  • Expository articles on seminal concepts from a rich variety of research fields
  • Written by distinguished researchers and exceptional speakers
  • Discusses fundamental research and new directions for growth
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About this book

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.

Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. Higher Structures in Geometry and Physics is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.

Contributors: L. Breen, A.S. Cattaneo, M. Cahen, V.A. Dolgushev, G. Felder, A. Giaquinto, S. Gutt, J. Huebschmann, T. Kadeishvili, H. Kajiura, B. Keller, Y. Kosmann-Schwarzbach, J.-L. Loday, S.A. Merkulov, D. Sternheimer, D.E. Tamarkin, C. Torossian, B.L. Tsygan, S. Waldmann, R.N. Umble.

Table of contents (16 chapters)

  • Topics in Algebraic Deformation Theory

    Giaquinto, Anthony

    Pages 1-24

  • Origins and Breadth of the Theory of Higher Homotopies

    Huebschmann, Johannes

    Pages 25-38

  • The Deformation Philosophy, Quantization and Noncommutative Space-Time Structures

    Sternheimer, Daniel

    Pages 39-56

  • Differential Geometry of Gerbes and Differential Forms

    Breen, Lawrence

    Pages 57-92

  • Symplectic Connections of Ricci Type and Star Products

    Cahen, Michel (et al.)

    Pages 93-110

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-0-8176-4735-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.00
price for USA
  • ISBN 978-0-8176-4734-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Higher Structures in Geometry and Physics
Book Subtitle
In Honor of Murray Gerstenhaber and Jim Stasheff
Editors
  • Alberto S. Cattaneo
  • Anthony Giaquinto
  • Ping Xu
Series Title
Progress in Mathematics
Series Volume
287
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-0-8176-4735-3
DOI
10.1007/978-0-8176-4735-3
Hardcover ISBN
978-0-8176-4734-6
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XV, 362
Number of Illustrations and Tables
92 b/w illustrations
Topics