Contents

Preface

ix

Plenary talks xi

Buildings, group extensions and the cohomology of congruence subgroups

ALEJANDRO ADEM

1

Heeke algebras acting on elliptic cohomology

ANDREW BAKER

17

Some root invariants and Steenrod operations in ExtA(F2, F2)

ROBERT

R.

BRUNER

27

Toward homology operations for mapping class groups

F.

R. COHEN AND ULRIKE TILLMANN

35

Spanier-Whitehead duality and critical points

0CTAVIAN CORNEA

47

Comparing completions of a space at a prime

PAUL GOERSS

65

Toward the homotopy groups of the higher real K-theory E02

VASSILY GORBOUNOV AND PETER SYMONDS

103

Skew symmetric bundle maps

DANIEL HENRY GOTTLIEB

117

The Adams spectral sequence for Minami's theorem

WEN-HSIUNG LIN AND MARK MAHOWALD

143

Applications of the Minami-Webb formula to splitting classifying spaces

JOHN MARTINO AND STEWART PRIDDY

179

Brave new worlds in stable homotopy theory

J. P. MAY

193

The stable splitting of

BM12

and related groups

R. JAMES MILGRAM AND C. OVERTON

213

On the Kervaire invariant problem

NORIHIKO MINAMI

229

vii