Contemporary Mathematics 1999; 378 pp; softcover Volume: 239 ISBN10: 082181057X ISBN13: 9780821810576 List Price: US$93 Member Price: US$74.40 Order Code: CONM/239
 This volume presents the proceedings of the conference held in honor of J. Michael Boardman's 60th birthday. It brings into print his classic work on conditionally convergent spectral sequences. Over the past 30 years, it has become evident that some of the deepest questions in algebra are best understood against the background of homotopy theory. Boardman and Vogt's theory of homotopytheoretic algebraic structures and the theory of spectra, for example, were two benchmark breakthroughs underlying the development of algebraic \(K\)theory and the recent advances in the theory of motives. The volume begins with short notes by Mac Lane, May, Stasheff, and others on the early and recent history of the subject. But the bulk of the volume consists of research papers on topics that have been strongly influenced by Boardman's work. Articles give readers a vivid sense of the current state of the theory of "homotopyinvariant algebraic structures". Also included are two major foundational papers by Goerss and Strickland on applications of methods of algebra (i.e., Dieudonné modules and formal schemes) to problems of topology. Boardman is known for the depth and wit of his ideas. This volume is intended to reflect and to celebrate those fine characteristics. Readership Graduate students and research mathematicians interested in the interaction between the theory of operads and mathematical physics; historical scientists interested in paradigm shifts; toplogists; algebraists; algebraic geometers. Table of Contents Some history  R. Thom  Note
 S. Mac Lane  Higher homotopies, pacts, and the bar construction
 J. P. May  The hare and the tortoise
 J. Morava  Cobordism of involutions revisited, revisited
 J. Stasheff  Grafting Boardman's cherry trees to quantum field theory
 R. M. Vogt  My time as Mike Boardman's student and our work on infinite loop spaces
Research papers  T. P. Bisson, D. J. Pengelley, and F. Williams  Stabilizing the lower operations for mod two cohomology
 J. M. Boardman  Conditionally convergent spectral sequences
 A. K. Bousfield  On \(K(n)\)equivalences of spaces
 S. L. Devadoss  Tessellations of moduli spaces and the mosaic operad
 P. G. Goerss  Hopf rings, Dieudonné modules, and \(E_\ast\Omega^2S^3\)
 M. Hovey and J. H. Palmieri  The structure of the Bousfield lattice
 P. Hu  Transfinite spectral sequences
 I. Kriz  The \(\mathbb{Z}/p\)equivariant complex cobordism ring
 K. Morisugi  Hopf constructions, Samelson products, and suspension maps
 D. Randall  Embedding homotopy spheres and the Kervaire invariant
 R. Schwänzl, R. M. Vogt, and F. Waldhausen  Adjoining roots of unity to \(E_\infty\) ring spectra in good casesA remark
 B. Steer and A. Wren  Grothendieck topology and the Picard group of a complex orbifold
 N. P. Strickland  Formal schemes and formal groups
 J. M. Turner  Simplicial commutative \(F_p\)algebras through the lookingglass of \(F_p\)local spaces
 A. A. Voronov  The Swisscheese operad
 W. S. Wilson  \(K(n + 1)\) equivalence implies \(K(n)\) equivalence
