Vol. 89, No. 1, 1980

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The relationship between Ljusternik-Schnirelman category and the concept of genus

Edward Richard Fadell

Vol. 89 (1980), No. 1, 33–42
Abstract

The concept of genus of an invariant, closed set A in a paracompact free G-space E is introduced for any compact Lie group G and the general result that G-genus A = catBA is proven where B = E∕G, A = E∕G and cat is short for Ljusternick-Schnirelman category. As a special case, the concept of genus (Krasnoselskii) coincides with the notion of category (Ljusternik-Schnirelman) as employed in a real or complex Banach space.

Mathematical Subject Classification 2000
Primary: 55M30
Milestones
Received: 19 March 1979
Revised: 9 May 1979
Published: 1 July 1980
Authors
Edward Richard Fadell