Higher Order Cohomology Operations in Local Coefficient Theory

1967 ◽  
Vol 89 (4) ◽  
pp. 909 ◽  
Author(s):  
Jerrold Siegel
Keyword(s):  
Higher Order ◽  
Local Coefficient ◽  
Cohomology Operations

On the differentials in the Adams spectral sequence

1964 ◽  
Vol 60 (3) ◽  
pp. 409-420 ◽  
Author(s):  
C. R. F. Maunder
Keyword(s):  
Spectral Sequence ◽  
Higher Order ◽  
Adams Spectral Sequence ◽  
Steenrod Algebra ◽  
Stable Homotopy ◽  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Stable Homotopy Groups ◽  
Cohomology Operations ◽  
Image Position

In this paper, we shall prove a result which identifies the differentials in the Adams spectral sequence (see (1,2)) with certain cohomology operations of higher kinds, in the sense of (4). This theorem will be stated precisely at the end of section 2, after a summary of the necessary information about the Adams spectral sequence and higher-order cohomology operations; the proof will follow in section 3. Finally, in section 4, we shall consider, by way of example, the Adams spectral sequence for the stable homotopy groups of spheres: we show how our theorem gives a proof of Liulevicius's result that , where the elements hn (n ≥ 0) are base elements ofcorresponding to the elements Sq2n in A, the mod 2 Steenrod algebra.

scholarly journals THE NONIMMERSION PROBLEM FOR RPn AND HIGHER-ORDER COHOMOLOGY OPERATIONS

1968 ◽  
Vol 60 (2) ◽  
pp. 432-437 ◽  
Author(s):  
S. Gitler ◽  
M. Mahowald ◽  
R. J. Milgram
Keyword(s):  
Higher Order ◽  
Cohomology Operations

Chern characters and higher-order cohomology operations

1964 ◽  
Vol 60 (4) ◽  
pp. 751-764 ◽  
Author(s):  
C. R. F. Maunder
Keyword(s):  
Higher Order ◽  
Chern Characters ◽  
Cohomology Operations

In this paper we shall show how a large number of higher-order cohomology operations (see (4)) may be calculated in suitable spaces by means of Chern characters: the method is an extension of that used by Adams in (1) to relate ‘mod p reductions’ of Chern characters and certain primary operations.

Massey products in K-theory

1970 ◽  
Vol 68 (2) ◽  
pp. 303-320 ◽  
Author(s):  
V. P. Snaith
Keyword(s):  
Vector Bundles ◽  
Higher Order ◽  
Massey Products ◽  
Cohomology Operations ◽  
K Theory

The aim of this paper is to reformulate the work of Massey(6), and Spanier(9, 10), on higher order cohomology operations, in terms of vector bundles in such a way as to produce geometrically some higher order operations in K-theory, which we will call Massey products.

Higher order track categories and the algebra of higher order cohomology operations

2010 ◽  
Vol 17 (1) ◽  
pp. 25-55
Author(s):  
Hans-Joachim Baues
Keyword(s):  
Spectral Sequence ◽  
Higher Order ◽  
Adams Spectral Sequence ◽  
Spectral Sequences ◽  
Differential Algebras ◽  
Cohomology Operations

Abstract We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an 𝑛-th order track category suitable for studying higher order Toda brackets and the differentials in spectral sequences. We describe various examples of higher order track categories which are topological, in particular the track category of higher cohomology operations. Also, differential algebras give rise to higher order track categories.

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