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.

Features:

• 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.

Readership

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