2012/05/03 by Jeffrey Strom, Strom, Jeffrey
Mathematics · #55S37 #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55S37
paper · pdf · doi:10.48550/arxiv.1205.0705
arXiv admin note: substantial text overlap with arXiv:1105.3951
arxiv created 2012/05/03 · openalex publication_date 2012/05/03 · arxiv updated 2012/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the theory of resolving classes, we show that if X is a CW complex of finite type such that \map_*(X, S2n+1)∼ * for all sufficiently large n, then \map_*(X, K) ∼ * for every simply-connected finite-dimensional CW complex K; and under mild hypotheses on π1(X), the same conclusion holds for all finite-dimensional complexes K. Since it is comparatively easy to prove the former condition for X = B\ZZ/p (we give a proof in an appendix), this result can be applied to give a new, more elementary proof of the Sullivan conjecture.