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Morse Theory and the Lusternik–Schnirelmann Category of Quaternionic Grassmannians

Part of: Global differential geometry Classical Topics in Algebraic Topology Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  25 October 2016

Enrique Macías-Virgós ,
María José Pereira-sáez  and
Daniel Tanré
Enrique Macías-Virgós
Affiliation:
Departamento de Xeometría e Topoloxía, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain (quique.macias@usc.es)
María José Pereira-sáez
Affiliation:
Facultade de Economía e Empresa, Universidade da Coruña, 15071 A Coruña, Spain (maria.jose.pereira@udc.es)
Daniel Tanré
Affiliation:
Département de Mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq Cedex, France (daniel.tanre@univ-lille1.fr)
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Abstract

The Lusternik–Schnirelmann category of the quaternionic Grassmannian

is known to be k(n − k). In this paper we show that this result can be deduced from Morse theory.

Keywords

Lusternik–Schnirelmann categoryGrassmann manifoldheight functionMorse–Bott theorycritical valueCayley transform

MSC classification

Secondary: 55M30: Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space 53C35: Symmetric spaces 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 2 , May 2017 , pp. 441 - 449
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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