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Homotopy Invariant Algebraic Structures: A Conference in Honor of J. Michael Boardman
Edited by: Jean-Pierre Meyer, Jack Morava, and W. Stephen Wilson, Johns Hopkins University, Baltimore, MD
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Contemporary Mathematics
1999; 378 pp; softcover
Volume: 239
ISBN-10: 0-8218-1057-X
ISBN-13: 978-0-8218-1057-6
List Price: US$88
Member Price: US$70.40
Order Code: CONM/239
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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 homotopy-theoretic 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 "homotopy-invariant 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 cases-A 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 looking-glass of \(F_p\)-local spaces
  • A. A. Voronov -- The Swiss-cheese operad
  • W. S. Wilson -- \(K(n + 1)\) equivalence implies \(K(n)\) equivalence
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