Moduli of spaces with prescribed homotopy groups

2017/05/16 by Piotr Pstrągowski, Pstrągowski, Piotr
Mathematics · #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1705.05761

openalex publication_date 2017/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a homotopy-theoretic approach to the theory of moduli of realizations of Blanc-Dwyer-Goerss, reproducing their obstructions to realizing a given Π-algebra as homotopy groups of a pointed space. Our techniques are based on the ∞-category P_Σ(Sph) of product-preserving presheaves on finite wedges of positive-dimensional spheres, leading to more conceptual and streamlined arguments.

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