منابع مشابه
An Adams Spectral Sequence Primer
My aim with these notes is to quickly get the student started with the Adams spectral sequence. To see its power requires that some concrete calculations be done. However, the algebra required can quickly become overwhelming if one starts with the generalized Adams spectral sequence. The classical Adams spectral sequence, in contrast, can be quickly set up and used to do some calculations which...
متن کاملOn the unstable Adams spectral sequence for SO and U , and splittings of unstable Ext groups ∗
Let U denote the category of unstable modules over the mod 2 Steenrod algebra A, and let Ext(−) = ExtsU(−,ΣZ2). Let M∞ = H̃∗(ΣCP∞ + ) denote the unstable A-module with nonzero classes xi such that i is odd and positive, and Sqx2k+1 = ( k j ) x2(j+k)+1. Then H∗(U) ≈ U(M∞), where the left side is the mod 2 cohomology of the infinite unitary group, and the right side the free unstable A-algebra gen...
متن کاملThe Motivic Adams Spectral Sequence
We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field of characteristic 0. Our results are based on computer calculations and a motivic version of the May spectral sequence. We discuss features of the associated Adams spectral sequence, and use these tools to give new proofs of some results in classical algebraic topology. We also consider a m...
متن کاملRoot Invariants in the Adams Spectral Sequence
Let E be a ring spectrum for which the E-Adams spectral sequence converges. We define a variant of Mahowald’s root invariant called the ‘filtered root invariant’ which takes values in the E1 term of the E-Adams spectral sequence. The main theorems of this paper concern when these filtered root invariants detect the actual root invariant, and explain a relationship between filtered root invarian...
متن کاملSquaring Operations in the Adams Spectral Sequence
I t has been long known that the cohomology H (A) of the mod 2 Steenrod algebra A admits squaring operations. (For example, see [ó].) Since H(A) is isomorphic to the £2 term of the mod 2 Adams spectral sequence [2], it is natural to inquire as to the relation of these squaring operations to the structure of the Adams spectral sequence. In this note we announce some results of this type extendin...
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ژورنال
عنوان ژورنال: Topology
سال: 1966
ISSN: 0040-9383
DOI: 10.1016/0040-9383(66)90025-5