Homotopy Invariant Algebraic Structures: A Conference in Honor of J. Michael Boardman
About this Title
Jean-Pierre Meyer, Jack Morava and W. Stephen Wilson, Editors
Publication: Contemporary Mathematics
Publication Year : Volume 239
ISBNs: 978-0-8218-1057-6 (print); 978-0-8218-7829-3 (online)
MathSciNet review: 1718068
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.
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
- René Thom – Letter from R. Thorn
- Saunders Mac Lane – Higher homotopies, pacts, and the bar construction
- J. P. May – The hare and the tortoise
- Jack Morava – Cobordism of involutions revisited, revisited [MR 1718072]
- Jim Stasheff – Grafting Boardman's cherry trees to quantum field theory [MR 1718073]
- R. M. Vogt – My time as Mike Boardman's student and our work on infinite loop spaces [MR 1718074]
- Terrence P. Bisson, David J. Pengelley and Frank Williams – Stabilizing the lower operations for mod two cohomology [MR 1718075]
- J. Michael Boardman – Conditionally convergent spectral sequences [MR 1718076]
- A. K. Bousfield – On -equivalences of spaces [MR 1718077]
- Satyan L. Devadoss – Tessellations of moduli spaces and the mosaic operad [MR 1718078]
- Paul G. Goerss – Hopf rings, Dieudonné modules, and [MR 1718079]
- Mark Hovey and John H. Palmieri – The structure of the Bousfield lattice [MR 1718080]
- Po Hu – Transfinite spectral sequences [MR 1718081]
- Igor Kriz – The -equivariant complex cobordism ring [MR 1718082]
- Kaoru Morisugi – Hopf constructions, Samelson products and suspension maps [MR 1718083]
- Duane Randall – Embedding homotopy spheres and the Kervaire invariant [MR 1718084]
- R. Schwänzl, R. M. Vogt and F. Waldhausen – Adjoining roots of unity to ring spectra in good cases—a remark [MR 1718085]
- Brian Steer and Andrew Wren – Grothendieck topology and the Picard group of a complex orbifold [MR 1718086]
- Neil P. Strickland – Formal schemes and formal groups [MR 1718087]
- James M. Turner – Simplicial commutative -algebras through the looking-glass of -local spaces [MR 1718088]
- Alexander A. Voronov – The Swiss-cheese operad [MR 1718089]
- W. Stephen Wilson – equivalence implies equivalence [MR 1718090]