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Regular Homotopy Classes of Singular Maps
Author(s) -
Juhász András
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504015102
Subject(s) - mathematics , homotopy , pure mathematics , mathematics subject classification , manifold (fluid mechanics) , classifying space , space (punctuation) , class (philosophy) , immersion (mathematics) , combinatorics , mechanical engineering , linguistics , philosophy , artificial intelligence , computer science , engineering
Two locally generic maps f , g : M n R 2n − 1 are regularly homotopic if they lie in the same path‐component of the space of locally generic maps. Our main result is that if n ≠ 3 and M n is a closed n ‐manifold then the regular homotopy class of every locally generic map f : M n R 2n − 1 is completely determined by the number of its singular points provided that f is singular (that is, f is not an immersion). 2000 Mathematics Subject Classification 57R45, 58K30, 57R42.