Electronic ISBN:  9780821878835 
Product Code:  CONM/293.E 
409 pp 
List Price:  $114.00 
MAA Member Price:  $102.60 
AMS Member Price:  $91.20 

Book DetailsContemporary MathematicsVolume: 293; 2002MSC: Primary 55; 57;
This volume presents the proceedings from the monthlong program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the JapanU.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.ReadershipGraduate students and research mathematicians interested in algebraic topology and homotopy theory.

Table of Contents

Two papers on the history of topology [ MR 1887523 ]

Haynes Miller  A marriage of manifolds and algebra: the mathematical work of Peter Landweber [ MR 1887524 ]

Norihiko Minami  Some mathematical influences of Stewart Priddy [ MR 1887525 ]

Research papers [ MR 1887523 ]

Martin Bendersky and Robert D. Thompson  Some properties of the $K$theory completion [ MR 1887526 ]

Robert R. Bruner, Donald M. Davis and Mark Mahowald  Nonimmersions of real projective spaces implied by $tmf$ [ MR 1887527 ]

Maurizio Brunetti  Higher Euler characteristics for almost extraspecial $p$groups [ MR 1887528 ]

Yutaka Hemmi  Unstable $p$th order operation and $H$spaces [ MR 1887529 ]

Mark Mahowald and Mike Hopkins  The structure of 24 dimensional manifolds having normal bundles which lift to $B{\rm O}[8]$ [ MR 1887530 ]

Po Hu and Igor Kriz  The homology of $BPO$ [ MR 1887531 ]

Masateru Inoue  $\scr A$generators of the cohomology of the Steinberg summand $M(n)$ [ MR 1890734 ]

James P. Lin  Commutators in the homology of $H$spaces [ MR 1890735 ]

James E. McClure and Jeffrey H. Smith  A solution of Deligne’s Hochschild cohomology conjecture [ MR 1890736 ]

Mamoru Mimura and Tetsu Nishimoto  Hopf algebra structure of Morava $K$theory of the exceptional Lie groups [ MR 1890737 ]

John Martino and Stewart Priddy  MinamiWebb type decompositions for compact Lie groups [ MR 1890738 ]

Douglas C. Ravenel  The method of infinite descent in stable homotopy theory. I [ MR 1890739 ]

Katsumi Shimomura  The homotopy groups $\pi _*(L_nT(m)\wedge V(n2))$ [ MR 1890740 ]

Dai Tamaki  The fiber of iterated Freudenthal suspension and Morava $K$theory of $\Omega ^kS^{2l+1}$ [ MR 1890741 ]

Michimasa Tanabe  On $K$flat and $K$moonshinelike elements in elliptic cohomology [ MR 1890742 ]

Takeshi Torii  The geometric fixed point spectrum of $({\bf Z}/p)^k$ Borel cohomology for $E_n$ and its completion [ MR 1890743 ]

Vladimir Voevodsky  A possible new approach to the motivic spectral sequence for algebraic $K$theory [ MR 1890744 ]

Clarence W. Wilkerson, Jr.  Rings of invariants and inseparable forms of algebras over the Steenrod algebra [ MR 1890745 ]

Nobuaki Yagita  Chow rings of classifying spaces of extraspecial $p$groups [ MR 1890746 ]


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This volume presents the proceedings from the monthlong program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the JapanU.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.
Graduate students and research mathematicians interested in algebraic topology and homotopy theory.

Two papers on the history of topology [ MR 1887523 ]

Haynes Miller  A marriage of manifolds and algebra: the mathematical work of Peter Landweber [ MR 1887524 ]

Norihiko Minami  Some mathematical influences of Stewart Priddy [ MR 1887525 ]

Research papers [ MR 1887523 ]

Martin Bendersky and Robert D. Thompson  Some properties of the $K$theory completion [ MR 1887526 ]

Robert R. Bruner, Donald M. Davis and Mark Mahowald  Nonimmersions of real projective spaces implied by $tmf$ [ MR 1887527 ]

Maurizio Brunetti  Higher Euler characteristics for almost extraspecial $p$groups [ MR 1887528 ]

Yutaka Hemmi  Unstable $p$th order operation and $H$spaces [ MR 1887529 ]

Mark Mahowald and Mike Hopkins  The structure of 24 dimensional manifolds having normal bundles which lift to $B{\rm O}[8]$ [ MR 1887530 ]

Po Hu and Igor Kriz  The homology of $BPO$ [ MR 1887531 ]

Masateru Inoue  $\scr A$generators of the cohomology of the Steinberg summand $M(n)$ [ MR 1890734 ]

James P. Lin  Commutators in the homology of $H$spaces [ MR 1890735 ]

James E. McClure and Jeffrey H. Smith  A solution of Deligne’s Hochschild cohomology conjecture [ MR 1890736 ]

Mamoru Mimura and Tetsu Nishimoto  Hopf algebra structure of Morava $K$theory of the exceptional Lie groups [ MR 1890737 ]

John Martino and Stewart Priddy  MinamiWebb type decompositions for compact Lie groups [ MR 1890738 ]

Douglas C. Ravenel  The method of infinite descent in stable homotopy theory. I [ MR 1890739 ]

Katsumi Shimomura  The homotopy groups $\pi _*(L_nT(m)\wedge V(n2))$ [ MR 1890740 ]

Dai Tamaki  The fiber of iterated Freudenthal suspension and Morava $K$theory of $\Omega ^kS^{2l+1}$ [ MR 1890741 ]

Michimasa Tanabe  On $K$flat and $K$moonshinelike elements in elliptic cohomology [ MR 1890742 ]

Takeshi Torii  The geometric fixed point spectrum of $({\bf Z}/p)^k$ Borel cohomology for $E_n$ and its completion [ MR 1890743 ]

Vladimir Voevodsky  A possible new approach to the motivic spectral sequence for algebraic $K$theory [ MR 1890744 ]

Clarence W. Wilkerson, Jr.  Rings of invariants and inseparable forms of algebras over the Steenrod algebra [ MR 1890745 ]

Nobuaki Yagita  Chow rings of classifying spaces of extraspecial $p$groups [ MR 1890746 ]