TY  - Type of reference 
TI  - Gysin-(ℤ/2ℤ)<sup><em>d</em></sup>-functors 
AU  - Dorra Bourguiba 
AU  - Said Zarati 
AB  - 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 &#120125;2-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 $$${\underset{i \geq 0}{\sum}}dim_{\mathbb{F}_{2}}H^{i}(X;\; \mathbb{F}_{2}) \geq 2^{d}$$$ 
DO  - 10.21494/ISTE.OP.2023.0939 
JF  - Advances in Pure and Applied Mathematics 
KW  - Elementary abelian 2-groups,  H∗(ℤ/2ℤ)<sup><em>d</em></sup>-modules, <multi>[en] H∗(ℤ/2ℤ)<sup><em>d</em></sup>− ,  Free actions of (ℤ/2ℤ)<sup><em>d</em></sup> on finite CW-complexes,  Equivariant cohomology,  Gysin exact sequence, Elementary abelian 2-groups,  H∗(ℤ/2ℤ)<sup><em>d</em></sup>-modules, <multi>[fr] H∗(ℤ/2ℤ)<sup><em>d</em></sup>− ,  Free actions of (ℤ/2ℤ)<sup><em>d</em></sup> on finite CW-complexes,  Equivariant cohomology,  Gysin exact sequence,  
L1  - https://www.openscience.fr/IMG/pdf/iste_apam23v14nspe_4.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2023/03/7 
SN  - 1869-6090 
TT  - Les foncteurs de type Gysin-(ℤ/2ℤ)<sup><em>d</em></sup> 
UR  - https://www.openscience.fr/Gysin-%E2%84%A4-2%E2%84%A4-d-functors 
IS  - Issue 2 (Special CSMT 2022) 
VL  - 14 
ER  -