The computation of Stiefel-Whitney classes

@article{Guillot2009TheCO,
  title={The computation of Stiefel-Whitney classes},
  author={Pierre Guillot},
  journal={arXiv: Algebraic Topology},
  year={2009}
}
  • Pierre Guillot
  • Published 19 May 2009
  • Mathematics
  • arXiv: Algebraic Topology
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here "compute" means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet… 
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References

SHOWING 1-10 OF 30 REFERENCES
The Evens-Kahn formula for the total Stiefel-Whitney class
Let G(X) denote the (augmented) multiplicative group of classical cohomology ring of a space X, with coefficients in Z/2. The (augmented) total Stiefel-Whitney class is a natural homomorphism w:
Transfers in the Group of Multiplicative Units of the Classical Cohomology Ring and Stiefel-Whitney Classes
It is proved that G(X)-the group of multiplicativ e units of the classical cohomology ring !!#»(*; Z/2) of a C^-complex X admits a transfer map N™: G(X)-+G(Y) defined 12=0 for finite coverings n :
The Chow ring of a classifying space
We define the Chow ring of the classifying space of a linear algebraic group. In all the examples where we can compute it, such as the symmetric groups and the orthogonal groups, it is isomorphic to
Unstable Modules over the Steenrod Algebra and Sullivan's Fixed Point Set Conjecture
An account of one of the main directions of algebraic topology, this book focuses on the Sullivan conjecture and its generalizations and applications. It gathers work on the theory of modules over
THE ADAMS CONJECTURE
On Chern classes of representations of finite groups
(cf. [8], say). Atiyah [ l ] posed the problem of relating the Chern classes of i{K with those of X, for any representation X of H. The purpose of this note is to announce the proof of a conjecture
Steenrod operations in chow theory
An action of the Steenrod algebra is constructed on the mod p Chow theory of varieties over a field of characteristic different from p, answering a question posed in Fulton's Intersection Theory. The
Calculating Group Cohomology: Tests for Completion
We want to calculate generators and relations for the mod- p cohomology rings of finite groups using computer technology. For this purpose we develop interactive tests to check whether a specific
Characteristic Classes and the Cohomology of Finite Groups
1. Group cohomology 2. Products and change of group 3. Relations with subgroups and duality 4. Spectral sequences 5. Representations and vector bundles 6. Bundles over the classifying space for a
Addendum to the paper: The Chow rings of G 2 and Spin(7)
Abstract The result in our article “The Chow rings of G 2 and Spin(7)” depends on a computation by Yagita, who in turn ascribes a critical contribution, concerning the Chow ring of Spin(7), to
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