2022/03/20 by Smail Benzakı, Benzaki, Smail, Youssef Ramı +1
Mathematics · #55M30 #55P62 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2203.10588
openalex publication_date 2022/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, using Sullivan's approach to rational homotopy theory of simply-connected finite type CW complexes, we endow the ℚ-vector space ExtC∗(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 make comparisons between 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.