On two results of Singhof

Augustin-Liviu Mare

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 379-383
  • ISSN: 0010-2628

Abstract

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For a compact connected semisimple Lie group G we shall prove two results (both related with Singhof’s paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of G , respectively the 1-dimensional relative category of a maximal torus T in G . The techniques will be classical, but we shall also apply some basic results concerning the so-called 𝒜 -category (cf. [14]).

How to cite

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Mare, Augustin-Liviu. "On two results of Singhof." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 379-383. <http://eudml.org/doc/248054>.

@article{Mare1997,
abstract = {For a compact connected semisimple Lie group $G$ we shall prove two results (both related with Singhof’s paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of $G$, respectively the 1-dimensional relative category of a maximal torus $T$ in $G$. The techniques will be classical, but we shall also apply some basic results concerning the so-called $\mathcal \{A\}$-category (cf. [14]).},
author = {Mare, Augustin-Liviu},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lusternik-Schnirelmann category; Lie groups; adjoint orbits; Lyusternik-Shnirel'man category; semisimple Lie group; coadjoint orbit},
language = {eng},
number = {2},
pages = {379-383},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On two results of Singhof},
url = {http://eudml.org/doc/248054},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Mare, Augustin-Liviu
TI - On two results of Singhof
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 379
EP - 383
AB - For a compact connected semisimple Lie group $G$ we shall prove two results (both related with Singhof’s paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of $G$, respectively the 1-dimensional relative category of a maximal torus $T$ in $G$. The techniques will be classical, but we shall also apply some basic results concerning the so-called $\mathcal {A}$-category (cf. [14]).
LA - eng
KW - Lusternik-Schnirelmann category; Lie groups; adjoint orbits; Lyusternik-Shnirel'man category; semisimple Lie group; coadjoint orbit
UR - http://eudml.org/doc/248054
ER -

References

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  9. Palais R.S., Terng C.L., Critical Point Theory and Submanifolds Geometry, Springer Verlag, 1988. MR0972503
  10. Pop I., Topologie Algebraică, Romanian Ed. Ştiinţifică, Bucureşti, 1990. MR1202715
  11. Postnikov M., Lie Groups and Lie Algebras, Mir Publishers, Moscow, 1986. Zbl0597.22001MR0905471
  12. Ramanujam S., Applications of Morse theory to some homogeneous spaces, Tohoku Math. J. 21 (1969), 343-354. (1969) 
  13. Singhof W., On the Lusternik-Schnirelmann category of Lie groups, Math. Z. 145 (1975), 111-116. (1975) Zbl0315.55012MR0391075

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