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Algebraic Topology
Edited by: Mark Mahowald and Stewart Priddy
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Contemporary Mathematics
1989; 350 pp; softcover
Volume: 96
ISBN-10: 0-8218-5102-0
ISBN-13: 978-0-8218-5102-9
List Price: US$60
Member Price: US$48
Order Code: CONM/96
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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

  • A. Adem, R. L. Cohen, and W. G. Dwyer -- Generalized Tate homology, homotopy fixed points and the transfer
  • D. J. Anick -- On the homogeneous invariants of a tensor algebra
  • A. Bahri, M. Bendersky, and P. Gilkey -- The relationship between complex bordism and \(K\)-theory for groups with periodic cohomology
  • A. Baker -- Elliptic cohomology, \(p\)-adic modular forms and Atkin's operator \(U_p\)
  • R. Brown -- Triadic Van Kampen theorems and Hurewicz theorem
  • D. Burghelea -- The free-loop space
  • D. P. Carlisle and N. J. Kuhn -- Smash products of summands of \(B(\Bbb Z/p)^n+\)
  • F. R. Cohen, R. L. Cohen, B. Mann, and R. J. Milgram -- Divisors and configuration on a surface
  • M. C. Crabb -- Periodicity in \(\Bbb Z/4\)-equivariant stable homotopy theory
  • E. B. Curtis and M. Mahowald -- The unstable Adams spectral sequence for \(S^3\)
  • D. H. Gottlieb -- Zeroes of pullback vector fields and fixed point theory for bodies
  • B. Gray -- Homotopy commutativity and the EHP sequence
  • J. R. Harper -- A proof of Gray's conjecture
  • H.-W. Henn, J. Lannes, and L. Schwartz -- Analytic functors, unstable algebras and cohomology of classifying spaces
  • L. Kauffman -- Statistical mechanics and the Alexander polynomial
  • J. Kulich -- A quotient of the iterated Singer construction
  • R. Lee and S. H. Weintraub -- A generalization of a theorem of Hecke to the Siegel space of degree two
  • W.-H. Lin -- A Koszul algebra whose cohomology is the \(E_3\)-term of the May spectral sequence for the Steenrod algebra
  • M. Mahowald and R. Thompson -- \(K\)-theory and unstable homotopy groups
  • H. Miller -- The elliptic character and the Witten genus
  • G. Mislin -- On the characteristic ring of flat bundles defined over a number field
  • N. Ray -- Loops on the \(3\)-sphere and umbral calculus
  • C. B. Thomas -- Characteristic classes and \(2\)-modular representations of some sporadic simple groups
  • T. Tsuboi -- On the connectivity of the classifying spaces for foliations
  • J. A. Wood -- Maximal abelian subgroups of Spinor groups and error-correcting codes
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