exit

Dorra Bourguiba
Université Tunis-ElManar
Tunisie

Said Zarati
Université Tunis-ElManar
Tunisie



Published on 7 March 2023   DOI : 10.21494/ISTE.OP.2023.0939

Abstract

Résumé

Keywords

Mots-clés

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:
(Cd):i0dimF2(Kd(0))i2d
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 i0dimF2Hi(X;F2)2d

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 :
(Cd):i0dimF2(Kd(0))i2d
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 i0dimF2Hi(X;F2)2d

Elementary abelian 2-groups H∗(ℤ/2ℤ)d-modules [en] H∗(ℤ/2ℤ)d Free actions of (ℤ/2ℤ)d on finite CW-complexes Equivariant cohomology Gysin exact sequence

Elementary abelian 2-groups H∗(ℤ/2ℤ)d-modules [fr] H∗(ℤ/2ℤ)d Free actions of (ℤ/2ℤ)d on finite CW-complexes Equivariant cohomology Gysin exact sequence

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