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On Topological Complexity of -mild spaces
Smail Benzaki, Youssef Rami
In this paper, we first prove the existence of relative free models of morphisms (resp. relative commutative models) in the category of (resp. ), where is a p…
On Topological Complexity of Gorenstein spaces
Smail Benzaki, Youssef Rami
In this paper, using Sullivan's approach to rational homotopy theory of simply-connected finite type CW complexes, we endow the -vector space $\mathcal{E}xt_{C^{\ast}(X…
A variant of the topological comlexity of a map
Youssef Rami, Younes Derfoufi
In this paper, we associate to two given continuous maps , on a path connected space , the relative topological complexity $TC^{(f, g, Z)}(X):=TC_X(X\times…
Gaps in the Milnor-Moore spectral sequence and the Hilali conjecture
Youssef Rami
In his study of Halperin's toral-rank conjecture, M. R. Hilali conjectured that for any simply connected rationally elliptic space , one must have $dimπ_*(X)\otimes \mathbb{Q} \…
A new invariant that's a lower bound of LS-category
Youssef Rami
Let be a simply connected CW-complex of finite type and any field. A first known lower bound of LS-category is the Toomer invariant (…