© 2011

Higher Structures in Geometry and Physics

In Honor of Murray Gerstenhaber and Jim Stasheff

  • Alberto S. Cattaneo
  • Anthony Giaquinto
  • Ping Xu


  • Expository articles on seminal concepts from a rich and variety of research fields

  • Written by distinguished researchers and exeptional speakers

  • Discusses fundamental research and new directions for growth


Part of the Progress in Mathematics book series (PM, volume 287)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Anthony Giaquinto
    Pages 1-24
  3. Michel Cahen, Simone Gutt, Stefan Waldmann
    Pages 93-110
  4. V. A. Dolgushev, D. E. Tamarkin, B. L. Tsygan
    Pages 139-158
  5. Johannes Huebschmann
    Pages 159-179
  6. T. Kadeishvili
    Pages 181-199
  7. Yvette Kosmann-Schwarzbach
    Pages 243-268
  8. Jean-Louis Loday
    Pages 269-292

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.


algebraic deformations cohomology homotopies

Editors and affiliations

  • Alberto S. Cattaneo
    • 1
  • Anthony Giaquinto
    • 2
  • Ping Xu
    • 3
  1. 1.Universität ZürichInstitut für MathematikZürichSwitzerland
  2. 2.Loyola University, ChicagoDepartment of MathematicsChicagoUSA
  3. 3.Pennsylvania State UniversityDepartment of MathematicsUniversity ParkUSA

Bibliographic information