Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Regular Homotopies of Low-Genus Non-Orientable Surfaces

Carlo H. Séquin

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2013-21
March 28, 2013

http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-21.pdf

This is a revised and extended version of Tech Report (EECS-2012-200) with the same title. The construction of various Klein bottles that belong to different regular homotopy classes, and which thus cannot be smoothly transformed into one another, is formally introduced. For all cases it is shown how these shapes can be partitioned into two Möbius bands and how the twistedness of these bands defines the homotopy type.


BibTeX citation:

@techreport{Séquin:EECS-2013-21,
    Author = {Séquin, Carlo H.},
    Title = {Regular Homotopies of Low-Genus Non-Orientable Surfaces},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2013},
    Month = {Mar},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-21.html},
    Number = {UCB/EECS-2013-21},
    Abstract = {This is a revised and extended version of Tech Report (EECS-2012-200) with the same title. The construction of various Klein bottles that belong to different regular homotopy classes, and which thus cannot be smoothly transformed into one another, is formally introduced. For all cases it is shown how these shapes can be partitioned into two Möbius bands and how the twistedness of these bands defines the homotopy type.}
}

EndNote citation:

%0 Report
%A Séquin, Carlo H.
%T Regular Homotopies of Low-Genus Non-Orientable Surfaces
%I EECS Department, University of California, Berkeley
%D 2013
%8 March 28
%@ UCB/EECS-2013-21
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-21.html
%F Séquin:EECS-2013-21