The Relationship between Ljusternik-Schnirelman Category and the Concept of Genus.
Abstract
The concept of genus of an invariant, closed set A in a paracompact free G-space E is introduced for any compact Lie groupd G and the general result that G-genus A = cat sub B A* is proven where B = E/G, A* = E/G and cat is short for Ljusternik-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. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1979
- Accession Number
- ADA068897
Entities
People
- Edward Fadell
Organizations
- University of Wisconsin–Madison