# 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 MÃ¶bius 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