Möbius Band as Simplicial Complex

Here we join up the top and bottom surfaces, but with a half twist. moebius topology
So we get a one sided surface with a single external boundary line. moebius

In the program FriCAS (described here) there is a function: moebiusBand which generates a minimal triangulation of a Möbius band.

Möbius band: One boundary, shown in red:

(2) -> moebiusBand()

        +1  2  3+
        |2  3  4|
   (2)  |3  4  5|
        |1  4  5|
        +1  2  5+
  Type: FiniteSimplicialComplex(VertexSetAbstract)

moebius band

This diagram can only be realised in 3D, to make it clearer in 2D I have duplicated nodes 3 and 4:

Möbius band

The blue arrows should join up, notice the head of the arrow is at the top on the left and bottom on the right.

More detail, for instance, mapping Möbius band to circle on page here.

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  5. Polynomials
  6. Topology

Chapter 6 - Topology. Contains a relatively gentle introduction to homology.


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