| Titre : |
Le théorème de Borsuk-Ulam pour les variétés de petite dimension. |
| Type de document : |
texte imprimé |
| Auteurs : |
Chahrazade Matmat, Auteur ; Fatiha Messaci, Directeur de thèse ; Christian Blanchet, Directeur de thèse |
| Mention d'édition : |
09/06/2021 |
| Editeur : |
جامعة الإخوة منتوري قسنطينة |
| Année de publication : |
2021 |
| Importance : |
123 f. |
| Format : |
30 cm. |
| Note générale : |
1 copies imprimées disponibles
|
| Langues : |
Français (fre) |
| Catégories : |
Français - Anglais
Mathématiques
|
| Tags : |
Mathématiques: Topologie Algébrique Le théorème de Borsuk-Ulam 3-variétés chirurgie forme d’enlacement Borsuk-Ulam Theorem 3-manifolds surgery linking forms
نظرية بورسوك-ايلام 3-متغيرات جراحة شكل التشابك |
| Index. décimale : |
510 Mathématiques |
| Résumé : |
We study the Borsuk-Ulam theorem for the triplet (M, τ, Rn), where M is a compact, connected, 3-manifold equipped with a fixed-point-free involution τ. The largest value of n for which the Borsuk-Ulam theorem holds is called the Z2-index and in our case it takes the value 1, 2 or 3. We fully discuss this index according to cohomological operations applied on the characteristic class x ∈ H1(N, Z2), where N = M/τ is the orbit space. In the oriented case, we obtain an expression of the index from the linking matrix of a surgery presentation of the orbit space. Recall that any oriented compact 3-manifold can be given such a surgery presentation. We apply our results to a few families of examples. As a warm up we first consider the double cover of lens spaces. We then fully discuss double covers of mapping tori. We consider the case of surgery presentations on algebraically split links. We finally study all free involutions on S1 × S2, which include a non oriented one. We prove the Borsuk-Ulam theorem for the non oriented 3-Klein bottle K3 with a natural involution.
|
| Diplôme : |
Doctorat en sciences |
| En ligne : |
../theses/math/MAT7771.pdf |
| Format de la ressource électronique : |
pdf |
| Permalink : |
index.php?lvl=notice_display&id=11604 |
Le théorème de Borsuk-Ulam pour les variétés de petite dimension. [texte imprimé] / Chahrazade Matmat, Auteur ; Fatiha Messaci, Directeur de thèse ; Christian Blanchet, Directeur de thèse . - 09/06/2021 . - جامعة الإخوة منتوري قسنطينة, 2021 . - 123 f. ; 30 cm. 1 copies imprimées disponibles
Langues : Français ( fre)
| Catégories : |
Français - Anglais
Mathématiques
|
| Tags : |
Mathématiques: Topologie Algébrique Le théorème de Borsuk-Ulam 3-variétés chirurgie forme d’enlacement Borsuk-Ulam Theorem 3-manifolds surgery linking forms
نظرية بورسوك-ايلام 3-متغيرات جراحة شكل التشابك |
| Index. décimale : |
510 Mathématiques |
| Résumé : |
We study the Borsuk-Ulam theorem for the triplet (M, τ, Rn), where M is a compact, connected, 3-manifold equipped with a fixed-point-free involution τ. The largest value of n for which the Borsuk-Ulam theorem holds is called the Z2-index and in our case it takes the value 1, 2 or 3. We fully discuss this index according to cohomological operations applied on the characteristic class x ∈ H1(N, Z2), where N = M/τ is the orbit space. In the oriented case, we obtain an expression of the index from the linking matrix of a surgery presentation of the orbit space. Recall that any oriented compact 3-manifold can be given such a surgery presentation. We apply our results to a few families of examples. As a warm up we first consider the double cover of lens spaces. We then fully discuss double covers of mapping tori. We consider the case of surgery presentations on algebraically split links. We finally study all free involutions on S1 × S2, which include a non oriented one. We prove the Borsuk-Ulam theorem for the non oriented 3-Klein bottle K3 with a natural involution.
|
| Diplôme : |
Doctorat en sciences |
| En ligne : |
../theses/math/MAT7771.pdf |
| Format de la ressource électronique : |
pdf |
| Permalink : |
index.php?lvl=notice_display&id=11604 |
|
Le théorème de Borsuk-Ulam pour les variétés de petite dimension.
