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)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1979
Accession Number
ADA068897

Entities

People

  • Edward Fadell

Organizations

  • University of Wisconsin–Madison

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Communities of Interest

  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Banach Space
  • Classification
  • Complex Numbers
  • Contracts
  • Inclusions
  • Lie Groups
  • Maps
  • Mathematics
  • Military Research
  • North Carolina
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  • Universities
  • Wisconsin

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Linear Algebra
  • Theoretical Analysis.

Technology Areas

  • Space