2010/02/10 by Toshihiro Yamaguchi, Yamaguchi, Toshihiro
Biochemistry, Genetics and Molecular Biology · Mathematics · #55P62 #55Q70 #55R15 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Sphingolipid Metabolism and Signaling #math.AT #msc:55P62 #msc:55Q70 #msc:55R15
paper · pdf · doi:10.48550/arxiv.1002.2032
first version
arxiv created 2010/02/10 · openalex publication_date 2010/02/10 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f:X→ Y be a pointed map between connected CW-complexes. As a generalization of the evaluation subgroup G_*(Y,X;f), we will define the \it relaxed evaluation subgroup \mathcal G_*(Y,X;f) in the homotopy group π_*(Y) of Y, which is identified with \rm Im π_*(ev) for the evaluation map ev :map(X,Y;f)× X→ Y given by ev (h,x)=h(x). Especially we see by using Sullivan model in rational homotopy theory for the rationalized map f\Q that \mathcal G_*(Y\Q,X\Q;f\Q)=π_*(Y)⊗ \Q if the map f induces an injection of rational homotopy groups. Also we compare it with more relaxed subgroups by several rationalized examples.