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Higher Homotopy Structures in Topology and Mathematical Physics
Edited by: John McCleary, Vassar College, Poughkeepsie, NY

Contemporary Mathematics
1999; 321 pp; softcover
Volume: 227
ISBN-10: 0-8218-0913-X
ISBN-13: 978-0-8218-0913-6
List Price: US$89
Member Price: US$71.20
Order Code: CONM/227
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Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on \(H\)-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas.


  • Accessible to a broad audience interested in mathematics and physics.
  • Offers a comprehensive overview of Stasheff's work.
  • Contains papers on very current research topics, including operads, combinatorial polyhedra, and moduli spaces.


Graduate students and research mathematicians working in topology, homological algebra and mathematical physics; physicists.

Table of Contents

  • J. McCleary -- An appreciation of the work of Jim Stasheff
  • M. Arkowitz and H. Scheerer -- The cohomology flat product and the Berstein algebra of a co-H-space
  • J. C. Becker and D. H. Gottlieb -- Spaces of local vector fields
  • T. Beke -- Operads from the viewpoint of categorical algebra
  • C. Berger -- Double loop spaces, braided monoidal categories and algebraic 3-type of space
  • L. A. Dickey -- Poisson brackets with divergence terms in field theories: Three examples
  • L. Friedlander and A. Schwarz -- Grassmannian and elliptic operators
  • M. Gerstenhaber and C. W. Wilkerson -- On the deformation of rings and algebras. V: Deformation of differential graded algebras
  • K. Hess -- Perturbation and transfer of generic algebraic structure
  • J. Huebschmann -- Extensions of Lie-Rinehart algebras and the Chern-Weil construction
  • I. M. James and W. Singhof -- On the category of fibre bundles, Lie groups, and Frobenius maps
  • M. M. Kapranov and M. Saito -- Hidden Stasheff polytopes in algebraic \(K\)-theory and in the space of Morse functions
  • T. Lada -- Commutators of \(A_\infty\) structures
  • M. Markl -- Simplex, associahedron, and cyclohedron
  • F. Neumann, M. D. Neusel, and L. Smith -- Rings of generalized and stable invariants and classifying spaces of compact Lie groups
  • D. Randall -- Block bundle origin of stable block bundle homotopy
  • J. A. Armario, P. Real, and B. Silva -- On \(p\)-minimal homological models of twisted tensor products of elementary complexes localised over a prime
  • A. A. Voronov -- Stability of the rational homotopy type of moduli spaces
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