منابع مشابه
Equivariant Stable Stems
Let S(r) denote the w-sphere with a linear involution having a fixed point set of codimension r, where O ^ r ^ w . We pick some fixed point as a base point and consider the set [S(r); S(t)] of base point preserving equivariant homotopy classes of maps from S(r) to S(t). This has a natural group structure for n—r^l and is abelian if n—r^2. There is a suspension functor S without action and one 2...
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For groups of prime order, equivariant stable maps between equivariant representation spheres are investigated using the Borel cohomology Adams spectral sequence. Features of the equivariant stable homotopy category, such as stability and duality, are shown to lift to the category of modules over the associated Steenrod algebra. The dependence on the dimension functions of the representations i...
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We will study equivariant homotopy theory for G a finite group (although this often easily generalizes to compact Lie groups). The general idea is that if we have two G-spaces X and Y , we’d like to study homotopy classes of equivariant maps between them: [X,Y ] = Map(X,Y )/htpy, where Map(X,Y ) = {f : X → Y |f(gx) = gf(x) for all g ∈ G}. In classical homotopy theory (i.e. when G is the trivial...
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Article history: Received 27 August 2008 Received in revised form 21 November 2008 Accepted 26 November 2008
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EQUIVARIANT stable homotopy theory was invented by G. B. Segal in the early 1970s [45]. He was motivated by his work with Atiyah [9] on equivariant K-theory, generalizing an earlier theorem of Atiyah’s on the K-theory of classifying spaces of finite groups to compact Lie groups, and by his work on configuration space and discrete models for iterated loop spaces. His work also suggested to him t...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1967
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1967-11713-0