Titre : Les foncteurs de type Gysin-(ℤ/2ℤ)d Auteurs : Dorra Bourguiba, Said Zarati, Revue : Avancées en Mathématiques Pures et Appliquées Numéro : Numéro 2 (Spécial CSMT 2022) Volume : 14 Date : 2023/03/7 DOI : 10.21494/ISTE.OP.2023.0939 ISSN : 1869-6090 Résumé : Let d ≥ 1 be an integer and Kd be a contravariant functor from the category of subgroups of (ℤ/2ℤ)d to the category of graded and finite 𝔽2-algebras. In this paper, we generalize the conjecture of G. Carlsson [C3], concerning free actions of (ℤ/2ℤ)d on finite CW-complexes, by suggesting, that if Kd is a Gysin-(ℤ/2ℤ)d-functor (that is to say, the functor Kd satisfies some properties, see 2.2), then we have : $$$\big(C_{d} \big): \; \underset{i \geq 0}{\sum}dim_{\mathbb{F}_{2}} \big(\mathcal{K}_{d}(0)\big)^{i} \geq 2^{d}$$$ We prove this conjecture for 1 ≤ d ≤ 3 and we show that, in certain cases, we get an independent proof of the following results (for d = 3 see [C4]) : If the group (ℤ/2ℤ)d, 1 ≤ d ≤ 3, acts freely and cellularly on a finite CW-complex X, then $$${\underset{i \geq 0}{\sum}}dim_{\mathbb{F}_{2}}H^{i}(X;\; \mathbb{F}_{2}) \geq 2^{d}$$$ Éditeur : ISTE OpenScience