On the Euler-Poincaré characteristics of a simply connected rationally elliptic CW-complex

2022/06/26 by Mahmoud Benkhalifa, Benkhalifa, Mahmoud
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2206.12804

openalex publication_date 2022/06/26 · openalex created_date 2022/06/30 · openalex updated_date 2026/07/28

Abstract

For a simply connected rationally elliptic CW-complex X, we show that the cohomology and the homotopy Euler-Poincaré characteristics are related to two new numerical invariants namely η_X and ρ_X which we define using the Whitehead exact sequences of the Quillen and the Sullivan models of X.

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