eBook ISBN:  9780821876848 
Product Code:  CONM/96.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876848 
Product Code:  CONM/96.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 96; 1989; 350 ppMSC: Primary 55; Secondary 57
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

Articles

A. Adem, R. L. Cohen and W. G. Dwyer — Generalized Tate homology, homotopy fixed points and the transfer [ MR 1022669 ]

David J. Anick — On the homogeneous invariants of a tensor algebra [ MR 1022670 ]

Anthony Bahri, Martin Bendersky and Peter Gilkey — The relationship between complex bordism and $K$theory for groups with periodic cohomology [ MR 1022671 ]

Andrew Baker — Elliptic cohomology, $p$adic modular forms and Atkin’s operator $U_p$ [ MR 1022672 ]

Ronald Brown — Triadic Van Kampen theorems and Hurewicz theorems [ MR 1022673 ]

D. Burghelea — The free loop space. I. Algebraic topology [ MR 1022674 ]

D. P. Carlisle and N. J. Kuhn — Smash products of summands of $B({\bf Z}/p)^n\,_+$ [ MR 1022675 ]

F. R. Cohen, R. L. Cohen, B. Mann and R. J. Milgram — Divisors and configurations on a surface [ MR 1022676 ]

M. C. Crabb — Periodicity in ${\bf Z}/4$equivariant stable homotopy theory [ MR 1022677 ]

Edward B. Curtis and Mark Mahowald — The unstable Adams spectral sequence for $S^3$ [ MR 1022678 ]

Daniel Henry Gottlieb — Zeroes of pullback vector fields and fixed point theory for bodies [ MR 1022679 ]

Brayton Gray — Homotopy commutativity and the $EHP$ sequence [ MR 1022680 ]

John R. Harper — A proof of Gray’s conjecture [ MR 1022681 ]

HansWerner Henn, Jean Lannes and Lionel Schwartz — Analytic functors, unstable algebras and cohomology of classifying spaces [ MR 1022682 ]

Louis H. Kauffman — Statistical mechanics and the Alexander polynomial [ MR 1022683 ]

James Kulich — A quotient of the iterated Singer construction [ MR 1022684 ]

Ronnie Lee and Steven H. Weintraub — A generalization of a theorem of Hecke to the Siegel space of degree two [ MR 1022685 ]

Wên Hsiung Lin — A Koszul algebra whose cohomology is the $E_3$term of the May spectral sequence for the Steenrod algebra [ MR 1022686 ]

Mark Mahowald and Robert Thompson — $K$theory and unstable homotopy groups [ MR 1022687 ]

Haynes Miller — The elliptic character and the Witten genus [ MR 1022688 ]

Guido Mislin — On the characteristic ring of flat bundles defined over a number field [ MR 1022689 ]

Nigel Ray — Loops on the $3$sphere and umbral calculus [ MR 1022690 ]

C. B. Thomas — Characteristic classes and $2$modular representations of some sporadic simple groups [ MR 1022691 ]

Takashi Tsuboi — On the connectivity of the classifying spaces for foliations [ MR 1022692 ]

Jay A. Wood — Maximal abelian subgroups of spinor groups and errorcorrecting codes [ MR 1022693 ]


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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.

Articles

A. Adem, R. L. Cohen and W. G. Dwyer — Generalized Tate homology, homotopy fixed points and the transfer [ MR 1022669 ]

David J. Anick — On the homogeneous invariants of a tensor algebra [ MR 1022670 ]

Anthony Bahri, Martin Bendersky and Peter Gilkey — The relationship between complex bordism and $K$theory for groups with periodic cohomology [ MR 1022671 ]

Andrew Baker — Elliptic cohomology, $p$adic modular forms and Atkin’s operator $U_p$ [ MR 1022672 ]

Ronald Brown — Triadic Van Kampen theorems and Hurewicz theorems [ MR 1022673 ]

D. Burghelea — The free loop space. I. Algebraic topology [ MR 1022674 ]

D. P. Carlisle and N. J. Kuhn — Smash products of summands of $B({\bf Z}/p)^n\,_+$ [ MR 1022675 ]

F. R. Cohen, R. L. Cohen, B. Mann and R. J. Milgram — Divisors and configurations on a surface [ MR 1022676 ]

M. C. Crabb — Periodicity in ${\bf Z}/4$equivariant stable homotopy theory [ MR 1022677 ]

Edward B. Curtis and Mark Mahowald — The unstable Adams spectral sequence for $S^3$ [ MR 1022678 ]

Daniel Henry Gottlieb — Zeroes of pullback vector fields and fixed point theory for bodies [ MR 1022679 ]

Brayton Gray — Homotopy commutativity and the $EHP$ sequence [ MR 1022680 ]

John R. Harper — A proof of Gray’s conjecture [ MR 1022681 ]

HansWerner Henn, Jean Lannes and Lionel Schwartz — Analytic functors, unstable algebras and cohomology of classifying spaces [ MR 1022682 ]

Louis H. Kauffman — Statistical mechanics and the Alexander polynomial [ MR 1022683 ]

James Kulich — A quotient of the iterated Singer construction [ MR 1022684 ]

Ronnie Lee and Steven H. Weintraub — A generalization of a theorem of Hecke to the Siegel space of degree two [ MR 1022685 ]

Wên Hsiung Lin — A Koszul algebra whose cohomology is the $E_3$term of the May spectral sequence for the Steenrod algebra [ MR 1022686 ]

Mark Mahowald and Robert Thompson — $K$theory and unstable homotopy groups [ MR 1022687 ]

Haynes Miller — The elliptic character and the Witten genus [ MR 1022688 ]

Guido Mislin — On the characteristic ring of flat bundles defined over a number field [ MR 1022689 ]

Nigel Ray — Loops on the $3$sphere and umbral calculus [ MR 1022690 ]

C. B. Thomas — Characteristic classes and $2$modular representations of some sporadic simple groups [ MR 1022691 ]

Takashi Tsuboi — On the connectivity of the classifying spaces for foliations [ MR 1022692 ]

Jay A. Wood — Maximal abelian subgroups of spinor groups and errorcorrecting codes [ MR 1022693 ]