On two results of Singhof
Commentationes Mathematicae Universitatis Carolinae (1997)
- Volume: 38, Issue: 2, page 379-383
- ISSN: 0010-2628
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topMare, 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
top- Borel A., Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts, Ann. Math. 57 (1953), 115-207. (1953) Zbl0052.40001MR0051508
- Bott R., Samelson H., Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964-1029. (1958) MR0105694
- Bröcker Th., tom Dieck T., Representations of Compact Lie Groups, Springer Verlag, 1985. MR0781344
- Clapp M., Puppe D., Invariants of the Lusternik-Schnirelmann type and the topology of critical sets, Trans. Amer. Math. Soc. 298 (1986), 604-620. (1986) Zbl0618.55003MR0860382
- Eilenberg S., Ganea T., On the Lusternik-Schnirelmann category of abstract groups, Ann. of Math. 65 (1957), 517-518. (1957) Zbl0079.25401MR0085510
- Fox R.H., On the Lusternik-Schnirelmann category, Ann. of Math. 42 (1941), 333-370. (1941) Zbl0027.43104MR0004108
- Ganea T., Lusternik-Schnirelmann category and strong category, Illinois J. Math. 11 (1967), 417-427. (1967) Zbl0149.40703MR0229240
- Hsiang W.Y., Palais R.S., Terng C.L., The topology of isoparametric submanifolds, J. Diff. Geom. 27 (1988), 423-461. (1988) Zbl0618.57018MR0940113
- Palais R.S., Terng C.L., Critical Point Theory and Submanifolds Geometry, Springer Verlag, 1988. MR0972503
- Pop I., Topologie Algebraică, Romanian Ed. Ştiinţifică, Bucureşti, 1990. MR1202715
- Postnikov M., Lie Groups and Lie Algebras, Mir Publishers, Moscow, 1986. Zbl0597.22001MR0905471
- Ramanujam S., Applications of Morse theory to some homogeneous spaces, Tohoku Math. J. 21 (1969), 343-354. (1969)
- Singhof W., On the Lusternik-Schnirelmann category of Lie groups, Math. Z. 145 (1975), 111-116. (1975) Zbl0315.55012MR0391075
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