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Recent Progress in Homotopy Theory

Edited by: Donald M. Davis Lehigh University, Bethlehem, PA
Jack Morava Johns Hopkins University, Baltimore, MD
Goro Nishida Kyoto University, Kyoto, Japan
W. Stephen Wilson Johns Hopkins University, Baltimore, MD
Nobuaki Yagita Ibaraki University, Ibaraki, Japan
Available Formats:
Electronic ISBN: 978-0-8218-7883-5
Product Code: CONM/293.E
409 pp
List Price: $114.00 MAA Member Price:$102.60
AMS Member Price: $91.20 Click above image for expanded view Recent Progress in Homotopy Theory Edited by: Donald M. Davis Lehigh University, Bethlehem, PA Jack Morava Johns Hopkins University, Baltimore, MD Goro Nishida Kyoto University, Kyoto, Japan W. Stephen Wilson Johns Hopkins University, Baltimore, MD Nobuaki Yagita Ibaraki University, Ibaraki, Japan Available Formats:  Electronic ISBN: 978-0-8218-7883-5 Product Code: CONM/293.E 409 pp  List Price:$114.00 MAA Member Price: $102.60 AMS Member Price:$91.20
• Book Details

Contemporary Mathematics
Volume: 2932002
MSC: Primary 55; 57;

This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.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 - Minami-Webb 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 $\pi _*(L_nT(m)\wedge V(n-2))$ [ 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 $K$-moonshine-like 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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Volume: 2932002
MSC: Primary 55; 57;

This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.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 - Minami-Webb 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 $\pi _*(L_nT(m)\wedge V(n-2))$ [ 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 $K$-moonshine-like 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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