Open AccessA Setting for A Theorem of Bott
Author(s) -
Marston Morse,
Stewart S. Cairns
Publication year - 1970
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.65.1.8
Subject(s) - corollary , mathematics , morse code , pure mathematics , homotopy , type (biology) , character (mathematics) , symbol (formal) , combinatorics , computer science , geometry , telecommunications , ecology , biology , programming language
Inspired by Theorem A of Raoul Bott,1 Morse and Cairns2 have stated Corollary 23.3 below, a theorem of essentially the same character as Theorem A of Bott. The symbol [unk] in Corollary 23.3 means that the sets to the left and right of [unk] have the samehomotopy type in the sense of Hilton (ref. 3, p. 3). Corollary 23.3 gives a setting to Bott's theorem in the theory of „bowls” introduced by Morse. The object of this note is to clarify and reinterpret the analysis presented as proof of Corollary 23.3 in reference 2.