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-2012-200
September 30, 2012

http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-200.pdf

The construction of various of 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-2012-200,
    Author = {Séquin, Carlo H.},
    Title = {Regular Homotopies of Low-Genus Non-Orientable Surfaces},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2012},
    Month = {Sep},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-200.html},
    Number = {UCB/EECS-2012-200},
    Abstract = {The construction of various of 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 2012
%8 September 30
%@ UCB/EECS-2012-200
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-200.html
%F Séquin:EECS-2012-200