On Topological Complexity of Gorenstein Spaces

In this paper, using Sullivan's approach to rational homotopy theory of simply-connected finite type CW complexes, we endow the Q-vector space Ext_C^(X;Q)(Q, C^(X;Q)) with a graded commutative algebra structure. This leads us to introduce the Ext-version of higher (resp. module, homology) topological complexity of X₀, the rationalization of X (resp. of X over Q). We then compare these invariants and their respective ordinary ones for Gorenstein spaces. We also highlight, in this context, the benefit of Adams-Hilton models over a field of odd characteristics especially through two cases, the first one when the space is a $2$-cell CW-complex and the second one when it is a suspension.