Osaka Journal of Mathematics

L'anneau de cohomologie des variétés de Seifert non-orientables

Anne Bauval and Claude Hayat

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If $p$ is a prime number, the cohomology ring with coefficients in $\mathbb{Z}/p\mathbb{Z}$ of an orientable or non-orientable Seifert manifold $M$ is obtained using a $\Delta$-simplicial decomposition of $M$. Several choices must be made before applying the Alexander-Whitney formula. The answers are given in terms of the classical cellular generators.


Si $p$ est un nombre premier, l'anneau de cohomologie à coefficients dans $\mathbb{Z}/p\mathbb{Z}$ d'une variété de Seifert $M$, orientable ou non-orientable est obtenu à partir d'une décomposition $\Delta$-simpliciale de $M$. Plusieurs choix sont à faire avant d'appliquer la formule d'Alexander-Whitney. Les réponses sont données en fonction des générateurs cellulaires classiques.

Article information

Osaka J. Math., Volume 54, Number 1 (2017), 157-195.

First available in Project Euclid: 3 March 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
Secondary: 55N45: Products and intersections 57S25: Groups acting on specific manifolds


Bauval, Anne; Hayat, Claude. L'anneau de cohomologie des variétés de Seifert non-orientables. Osaka J. Math. 54 (2017), no. 1, 157--195.

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