Steenrod operations in Chow theory
نویسندگان
چکیده
منابع مشابه
Steenrod operations on the Chow ring of a classifying space
We use the Steenrod algebra to study the Chow ring CH∗BG of the classifying space of an algebraic group G. We describe a localization property which relates a given G to its elementary abelian subgroups, and we study a number of particular cases, namely symmetric groups and Chevalley groups. It turns out that the Chow rings of these groups are completely determined by the abelian subgroups and ...
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In this paper I give new proofs of the structure theorems for the unoriented cobordism ring [12] and the complex cobordism ring [8, 131. The proofs are elementary in the sense that no mention of the Steenrod algebra or Adams spectral sequence is made. In fact, the only result from homotopy theory which is used in an essential way is the Serre finiteness theorem in order to know that the complex...
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Let G be a compact connected Lie group andH the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan
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For a commutative Hopf algebra A over Z/p, where p is a prime integer, we define the Steenrod operations P i in cyclic cohomology of A using a tensor product of a free resolution of the symmetric group S n and the standard resolution of the algebra A over the cyclic category according to Loday (1992). We also compute some of these operations. 1. Introduction. For any prime p, the mod p Steenrod...
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We present a formula describing the action of a generalised Steenrod operation of Z2-type [14] on the cohomology class represented by a proper self-transverse immersion f : M X. Our formula depends only on the Umkehr map, the characteristic classes of the normal bundle, and the class represented by the double point immersion of f . This generalises a classical result of R. Thom [13]: If α ∈ H(X...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2003
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-03-03224-0