Lusternik-Schnirelmann category of non-simply connected compact simple Lie groups

Norio Iwase, Mamoru Mimura, Tetsu Nishimoto

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14 Citations (Scopus)


Let F → 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 cat (PU(n)) ≤ 3(n - 1) for all n ≥ 1, which might be best possible, since we have cat (PU(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.

Original languageEnglish
Pages (from-to)111-123
Number of pages13
JournalTopology and its Applications
Issue number1-3
Publication statusPublished - May 14 2005

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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