# The computation of Stiefel-Whitney classes

Pierre Guillot^{[1]}

- [1] Université de Strasbourg-CNRS IRMA 7 rue René Descartes 67084 Strasbourg (France)

Annales de l’institut Fourier (2010)

- Volume: 60, Issue: 2, page 565-606
- ISSN: 0373-0956

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topGuillot, Pierre. "The computation of Stiefel-Whitney classes." Annales de l’institut Fourier 60.2 (2010): 565-606. <http://eudml.org/doc/116282>.

@article{Guillot2010,

abstract = {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).Next, we give an application: thanks to the new information gathered, we can in many cases determine which cohomology classes are supported by algebraic varieties.},

affiliation = {Université de Strasbourg-CNRS IRMA 7 rue René Descartes 67084 Strasbourg (France)},

author = {Guillot, Pierre},

journal = {Annales de l’institut Fourier},

keywords = {Cohomology of groups; characteristic classes; algorithms; computers; chow rings; Steenrod algebras; cohomology of groups; computation; Chow rings; cohomology rings; Stiefel-Whitney classes; Steenrod operations},

language = {eng},

number = {2},

pages = {565-606},

publisher = {Association des Annales de l’institut Fourier},

title = {The computation of Stiefel-Whitney classes},

url = {http://eudml.org/doc/116282},

volume = {60},

year = {2010},

}

TY - JOUR

AU - Guillot, Pierre

TI - The computation of Stiefel-Whitney classes

JO - Annales de l’institut Fourier

PY - 2010

PB - Association des Annales de l’institut Fourier

VL - 60

IS - 2

SP - 565

EP - 606

AB - 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).Next, we give an application: thanks to the new information gathered, we can in many cases determine which cohomology classes are supported by algebraic varieties.

LA - eng

KW - Cohomology of groups; characteristic classes; algorithms; computers; chow rings; Steenrod algebras; cohomology of groups; computation; Chow rings; cohomology rings; Stiefel-Whitney classes; Steenrod operations

UR - http://eudml.org/doc/116282

ER -

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