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

Norio Iwase, Mamoru Mimura, Tetsu Nishimoto

研究成果: ジャーナルへの寄稿記事

11 引用 (Scopus)

抄録

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.

元の言語英語
ページ(範囲)111-123
ページ数13
ジャーナルTopology and its Applications
150
発行部数1-3
DOI
出版物ステータス出版済み - 5 14 2005

Fingerprint

Lusternik-Schnirelmann Category
Simple group
Analytic group
Compatibility Conditions
Fiber Bundle
Less than or equal to
Cone
Decompose

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

これを引用

Lusternik-Schnirelmann category of non-simply connected compact simple Lie groups. / Iwase, Norio; Mimura, Mamoru; Nishimoto, Tetsu.

:: Topology and its Applications, 巻 150, 番号 1-3, 14.05.2005, p. 111-123.

研究成果: ジャーナルへの寄稿記事

Iwase, Norio ; Mimura, Mamoru ; Nishimoto, Tetsu. / Lusternik-Schnirelmann category of non-simply connected compact simple Lie groups. :: Topology and its Applications. 2005 ; 巻 150, 番号 1-3. pp. 111-123.
@article{ce2a52a0e34d43fb8af01d10ff3d590a,
title = "Lusternik-Schnirelmann category of non-simply connected compact simple Lie groups",
abstract = "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.",
author = "Norio Iwase and Mamoru Mimura and Tetsu Nishimoto",
year = "2005",
month = "5",
day = "14",
doi = "10.1016/j.topol.2004.11.006",
language = "English",
volume = "150",
pages = "111--123",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",
number = "1-3",

}

TY - JOUR

T1 - Lusternik-Schnirelmann category of non-simply connected compact simple Lie groups

AU - Iwase, Norio

AU - Mimura, Mamoru

AU - Nishimoto, Tetsu

PY - 2005/5/14

Y1 - 2005/5/14

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=17444373099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17444373099&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2004.11.006

DO - 10.1016/j.topol.2004.11.006

M3 - Article

AN - SCOPUS:17444373099

VL - 150

SP - 111

EP - 123

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 1-3

ER -