Secondary cohomology operations applied to the Thom class

1980 ◽  
pp. 442-455
Author(s):  
Friedrich Hegenbarth
Keyword(s):  
Thom Class ◽  
Cohomology Operations

scholarly journals Secondary cohomology operations on the Thom class

Topology ◽  
1963 ◽  
Vol 2 (4) ◽  
pp. 367-377 ◽  
Author(s):  
Mark E. Mahowald ◽  
Franklin P. Peterson
Keyword(s):  
Thom Class ◽  
Cohomology Operations

scholarly journals A note on immersing manifolds in euclidean spaces

1987 ◽  
Vol 36 (2) ◽  
pp. 215-226
Author(s):  
Ng Tze Beng
Keyword(s):  
Normal Bundle ◽  
Euclidean Spaces ◽  
Thom Class ◽  
Dyadic Expansion ◽  
Cohomology Operations ◽  
General Manifold

Let M be a closed, connected smooth and 3-connected mod 2 (that is Hi(M;ℤ2) = 0, 0 < i ≤ 3) manifold of dimension n = 7 + 8k. Using a combination of cohomology operations on certain cohomology classes of M and on the Thom class of the stable normal bundle of M we show that under certain conditions M immerses in R2n−8. This extends previously known results for such a general manifold when the number of 1's in the dyadic expansion of n is less than 8.

scholarly journals A Conjecture on Homotopy Groups of Spheres, Details on the Algebra of Higher Cohomology Operations

2009 ◽  
Vol 16 (1) ◽  
pp. 1-12
Author(s):  
Hans-Joachim Baues
Keyword(s):  
Homotopy Groups ◽  
Homotopy Groups Of Spheres ◽  
Cohomology Operations

Abstract The computation of the algebra of secondary cohomology operations in [Baues, The algebra of secondary cohomology operations, Birkhäuser Verlag, 2006] leads to a conjecture concerning the algebra of higher cohomology operations in general and an Ext-formula for the homotopy groups of spheres. This conjecture is discussed in detail in this paper.

scholarly journals Higher cohomology operations and R–completion

2018 ◽  
Vol 18 (1) ◽  
pp. 247-312 ◽  
Author(s):  
David Blanc ◽  
Debasis Sen
Keyword(s):  
Cohomology Operations

scholarly journals Book Review: Cohomology operations and applications in homotopy theory

1969 ◽  
Vol 75 (5) ◽  
pp. 929-930
Author(s):  
M. Mahowald
Keyword(s):  
Homotopy Theory ◽  
Cohomology Operations

Functional Cohomology Operations and Relations

1965 ◽  
Vol 87 (3) ◽  
pp. 649 ◽  
Author(s):  
Jean-Pierre Meyer
Keyword(s):  
Cohomology Operations

Secondary Cohomology Operations: Two Formulas

1959 ◽  
Vol 81 (2) ◽  
pp. 281 ◽  
Author(s):  
F. P. Peterson ◽  
N. Stein
Keyword(s):  
Cohomology Operations

An Overview of the Proof

2019 ◽  
pp. 3-22
Author(s):  
Christian Haesemeyer ◽  
Charles A. Weibel
Keyword(s):  
Motivic Cohomology ◽  
Norm Residue ◽  
Cohomology Operations ◽  
Definition Of ◽  
Special Case

This chapter provides the main steps in the proof of Theorems A and B regarding the norm residue homomorphism. It also proves several equivalent (but more technical) assertions in order to prove the theorems in question. This chapter also supplements its approach by defining the Beilinson–Lichtenbaum condition. It thus begins with the first reductions, the first of which is a special case of the transfer argument. From there, the chapter presents the proof that the norm residue is an isomorphism. The definition of norm varieties and Rost varieties are also given some attention. The chapter also constructs a simplicial scheme and introduces some features of its cohomology. To conclude, the chapter discusses another fundamental tool—motivic cohomology operations—as well as some historical notes.

The Thom Class and Localization

1999 ◽  
pp. 149-172
Author(s):  
Victor W. Guillemin ◽  
Shlomo Sternberg ◽  
Jochen Brüning
Keyword(s):  
Thom Class
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