Contemporary Mathematics 2002; 409 pp; softcover Volume: 293 ISBN10: 0821828010 ISBN13: 9780821828014 List Price: US$114 Member Price: US$91.20 Order Code: CONM/293
 This volume presents the proceedings from the monthlong program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the JapanU.S. Mathematics Institute (JAMI). The book centers on the following: 1. classical and nonclassical theory of \(H\)spaces, compact groups, and finite groups, 2. classical and chromatic homotopy theory and localization, 3. classical and topological Hochschild cohomology, 4. elliptic cohomology and its relation to Moonshine and topological modular forms, and 5. motivic cohomology and Chow rings. It surveys the current state of research in homotopy theory and suggests a framework for future developments. The book begins with two historical accounts, of the work of Professors Peter Landweber and Stewart Priddy, in honor of their sixtieth birthdays. Readership Graduate students and research mathematicians interested in algebraic topology and homotopy theory. Table of Contents Two papers on the history of topology  H. Miller  A marriage of manifolds and algebra: The mathematical work of Peter Landweber
 N. Minami  Some mathematical influences of Stewart Priddy
Research papers  M. Bendersky and R. D. Thompson  Some properties of the \(K\)theory completion
 R. R. Bruner, D. M. Davis, and M. Mahowald  Nonimmersions of real projective spaces implied by \(tmf\)
 M. Brunetti  High Euler characteristics for almost extraspecial \(p\)groups
 Y. Hemmi  Unstable \(p\)th order operation and \(H\)spaces
 M. Mahowald and M. Hopkins  The structure of 24 dimensional manifolds having normal bundles which lift to \(BO[8]\)
 P. Hu and I. Kriz  The homology of \(BPO\)
 M. Inoue  \(\mathcal{A}\)generators of the cohomology of the Steinberg summand \(M(n)\)
 J. P. Lin  Commutators in the homology of \(H\)spaces
 J. E. McClure and J. H. Smith  A solution of Deligne's Hochschild cohomology conjecture
 M. Mimura and T. Nishimoto  Hopf algebra structure of Morava \(K\)theory of the exceptional Lie groups
 J. Martino and S. Priddy  MinamiWebb type decompositions for compact Lie groups
 D. C. Ravenel  The method of infinite descent in stable homotopy theory I
 K. Shimomura  The homotopy groups \(\pi_*(L_nT(m)\wedge V(n2))\)
 D. Tamaki  The fiber of iterated Freudenthal suspension and Morava Ktheory of \(\Omega^kS^{2\ell+1}\)
 M. Tanabe  On \(K\)flat and \(K\)moonshinelike elements in elliptic cohomology
 T. Torii  The geometric fixed point spectrum of \(({\mathbf Z}/p)^k\) Borel cohomology for \(E_n\) and its completion
 V. Voevodsky  A possible new approach to the motivic spectral sequence for algebraic Ktheory
 C. W. Wilkerson, Jr.  Rings of invariants and inseparable forms of algebras over the Steenrod algebra
 N. Yagita  Chow rings of classifying spaces of extraspecial \(p\) groups
