# Algebraic Topology

Share this page *Edited by *
*Mark Mahowald; Stewart Priddy*

This book will provide readers with an overview of some of the major
developments in current research in algebraic topology. Representing some of
the leading researchers in the field, the book contains the proceedings of the
International Conference on Algebraic Topology, held at Northwestern University
in March, 1988. Several of the lectures at the conference were expository and
will therefore appeal to topologists in a broad range of areas.

The primary emphasis of the book is on homotopy theory and its applications.
The topics covered include elliptic cohomology, stable and unstable homotopy
theory, classifying spaces, and equivariant homotopy and cohomology. Geometric
topics—such as knot theory, divisors and configurations on surfaces,
foliations, and Siegel spaces—are also discussed. Researchers wishing to
follow current trends in algebraic topology will find this book a valuable
resource.

# Table of Contents

## Algebraic Topology

- Contents ix10 free
- Preface xi12 free
- Plenary talk titles xiii14 free
- Generalized Tate homology, homotopy fixed points and the transfer 116 free
- On the homogeneous invariants of a tensor algebra 1530
- The relationship between complex bordism and K -theory for groups with periodic cohomology 1934
- Elliptic cohomology, p-adic modular forms and Atkin's operator Up 3348
- Triadic Van Kampen theorems and Hurewicz theorems 3954
- The free loop space 5974
- Smash products of summands of B(Z/p)n + 87102
- Divisors and configurations on a surface 103118
- Periodicity in Z / 4-equivariant stable homotopy theory 109124
- The unstable Adams spectral sequence for S3 125140
- Zeroes of pullback vector fields and fixed point theory for bodies 163178
- Homotopy commutativity and the EHP sequence 181196
- A proof of Gray's conjecture 189204
- Analytic functors, unstable algebras and cohomology of classifying spaces 197212
- Statistical mechanics and the Alexander polynomial 221236
- A quotient of the iterated Singer construction 233248
- A generalization of a theorem of Heeke to the Siegel space of degree two 243258
- A Koszul algebra whose cohomology is the E3-term of the May spectral sequence for the Steenrod algebra 261276
- K-theory and unstable homotopy groups 273288
- The elliptic character and the Witten genus 281296
- On the characteristic ring of flat bundles defined over a number field 291306
- Loops on the 3-sphere and umbral calculus 297312
- Characteristic classes and 2-modular representations of some sporadic simple groups 303318
- On the connectivity of the classifying spaces for foliations 319334
- Maximal abelian subgroups of Spinor groups and error-correcting codes 333348