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Mathematical Sciences: Finite Groups and Complex Oriented Theories in Homotopy

Mathematical Sciences: Finite Groups and Complex Oriented Theories in Homotopy
数学科学:同伦中的有限群和复向理论
批准号:
8802411
负责人:
Nicholas Kuhn
金额:
$8.94万
依托单位国家:
美国
项目类别:
Continuing Grant
财政年份:
1988
资助国家:
美国
项目状态:
已结题
起止时间:
1988-06-01 至 1992-11-30

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中文摘要
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英文摘要
Group theoretic constructions have traditionally been part of the arsenal of an algebraic topologist . On the most basic level, tools from (finite) group theory have been used to construct topological tools: Steenrod squares, characteristic classes, spaces with A(n)-free cohomology, etc. On a more subtle level, many basic topological structures seem to be determined by group theoretic structures - for example, infinite loop space structures are determined by the combinatorics of the symmetric groups, and the theorem of Atiyah that calculates K(BG), says that group theory determines this ring. Nicholas J. Kuhn's recent and current research continues this tradition of using group theory to guide one's study of topological questions. In particular, in his ongoing collaboration with M. Hopkins and D. Ravenel, a combination of group theory, equivariant homotopy, and number theory is being used to gain greater understanding of the "geometry" underlying complex oriented cohomology theories. These include, in particular, the Morava K-theories - known by the work of E. Devinatz, Hopkins, and J. Smith to be of central importance in stable homotopy theory.
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FRG: Collaborative Research: The Calculus of Functors and the Theory of Operads: Interactions and Applications
  • 批准号:
    0967649
  • 项目类别:
    Standard Grant
  • 资助金额:
    $41.2万
  • 财政年份:
    2010
  • 负责人:
    Nicholas Kuhn
  • 依托单位:
Problems in Homotopy Theory and Group Cohomology
  • 批准号:
    0604206
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $16.0万
  • 财政年份:
    2006
  • 负责人:
    Nicholas Kuhn
  • 依托单位:
Problems in Homotopy, K-theory, and Representation Theory
  • 批准号:
    0100710
  • 项目类别:
    Continuing Grant
  • 资助金额:
    $23.76万
  • 财政年份:
    2001
  • 负责人:
    Nicholas Kuhn
  • 依托单位:
New Problems in Homotopy, K-Theory, and Representation Theory
  • 批准号:
    9802493
  • 项目类别:
    Standard Grant
  • 资助金额:
    $8.4万
  • 财政年份:
    1998
  • 负责人:
    Nicholas Kuhn
  • 依托单位:
国内基金
海外基金
Handbook of the Mathematics of the Arts and Sciences的中文翻译
  • 批准号:
    12226504
  • 项目类别:
    数学天元基金项目
  • 资助金额:
    20.0万元
  • 批准年份:
    2022
  • 负责人:
    黄朝凌
  • 依托单位:
SCIENCE CHINA: Earth Sciences
Journal of Environmental Sciences
SCIENCE CHINA Information Sciences