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Recent Progress in Homotopy Theory
Edited by: Donald M. Davis, Lehigh University, Bethlehem, PA, Jack Morava, Johns Hopkins University, Baltimore, MD, Goro Nishida, Kyoto University, Japan, W. Stephen Wilson, Johns Hopkins University, Baltimore, MD, and Nobuaki Yagita, Ibaraki University, Japan
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Contemporary Mathematics
2002; 409 pp; softcover
Volume: 293
ISBN-10: 0-8218-2801-0
ISBN-13: 978-0-8218-2801-4
List Price: US$114 Member Price: US$91.20
Order Code: CONM/293

This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.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.

Graduate students and research mathematicians interested in algebraic topology and homotopy theory.

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 -- Minami-Webb type decompositions for compact Lie groups
• D. C. Ravenel -- The method of infinite descent in stable homotopy theory I
• K. Shimomura -- The homotopy groups $$\pi_*(L_nT(m)\wedge V(n-2))$$
• D. Tamaki -- The fiber of iterated Freudenthal suspension and Morava K-theory of $$\Omega^kS^{2\ell+1}$$
• M. Tanabe -- On $$K$$-flat and $$K$$-moonshine-like 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 K-theory
• 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