# Recent Progress in Homotopy Theory

Share this page *Edited by *
*Donald M. Davis; Jack Morava; Goro Nishida; W. Stephen Wilson; Nobuaki Yagita*

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.

#### Readership

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

# Table of Contents

## Recent Progress in Homotopy Theory

- Contents vii8 free
- Preface ix10 free
- Two papers on the history of topology 112 free
- Research papers 3344
- Some properties of the K-theory completion 3546
- Nonimmersions of real projective spaces implied by tm f 4556
- Higher Euler characteristics for almost extraspecial p-groups 6980
- Unstable p-th order operation and H-spaces 7586
- The structure of 24 dimensional manifolds having normal bundles which lift to BO[8] 89100
- The homology of BPO 111122
- A-generators of the cohomology of the Steinberg summand M(n) 125136
- Commutators in the homology of H -spaces 141152
- A solution of Deligne's Hochschild cohomology conjecture 153164
- Hopf algebra structure of Morava K-theory of the exceptional Lie groups 195206
- Minami-Webb type decompositions for compact Lie groups 233244
- The method of infinite descent in stable homotopy theory I 251262
- The homotopy groups π*(LnT(m) Λ V(n – 2)) 285296
- The Fiber of iterated Freudenthal suspension and Morava K-theory of ΩkS2ℓ+1 299310
- On K-flat and K-moonshine-like elements in elliptic cohomology 331342
- The geometric fixed point spectrum of (Z/p)k Borel cohomology for En and its completion 343354
- A possible new approach to the motivic spectral sequence for algebraic K-theory 371382
- Rings of invariants and inseparable forms of algebras over the Steenrod algebra 381392
- Chow rings of classifying spaces of extraspecial p groups 397408