2003/03/07 by Norio Iwase, Iwase, Norio, Mamoru Mimura +3
Mathematics · Medicine · #22E20 #55M30 #57N60 #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Ophthalmology and Eye Disorders #math.AT #msc:22E20 #msc:55M30 #msc:57N60
paper · pdf · doi:10.48550/arxiv.math/0303085
13 pages
openalex publication_date 2003/03/07 · arxiv created 2004/11/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let F \hookrightarrow X → B be a fibre bundle with structure group G, where B is (d-1)-connected and of finite dimension, d ≥ 1. We prove that the strong L-S category of X is less than or equal to m + (dim B)/(d), if F has a cone decomposition of length m under a compatibility condition with the action of G on F. This gives a consistent prospect to determine the L-S category of non-simply connected Lie groups. For example, we obtain \catPU(n) ≤ 3(n-1) for all n ≥ 1, which might be best possible, since we have \catPU(pr)=3(pr-1) for any prime p and r ≥ 1. Similarly, we obtain the L-S category of SO(n) for n ≤ 9 and PO(8). We remark that all the above Lie groups satisfy the Ganea conjecture on L-S category.