2003/11/27 by Julio Rubio Garcia, Julio [0000-0002-4282-3692] Rubio García, Garcia, Julio Rubio +2
Mathematics · #18D50 #55-04 #55P15 #55S45 #55Txx #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:18D50 #msc:55-04 #msc:55P15 #msc:55S45 #msc:55Txx
paper · pdf · doi:10.48550/arxiv.math/0311509
Submitted to HHA in October 2003
arxiv created 2003/11/27 · openalex publication_date 2003/11/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The classical problem of algebraic models for homotopy types is precisely stated, to our knowledge for the first time. Two different natural statements for this problem are produced, the simplest one being entirely solved by the notion of SSEH-structure, due to the authors. Other tentative solutions, Postnikov towers and E_∞-chain complexes, are considered and compared with the SSEH-structures. In particular, which looks at least like an unfortunate imprecision in the usual definition of the k-``invariants'' is explained, which implies we seem far from a solution for the ideal statement of our problem. At the positive side, the problem of the computability of the Postnikov towers is solved.