Riemann Surfaces

Möbius Strip

Here is a visualisation of an example of a 2-dimensional non-orientable Riemann surface: the Möbius strip. You can magnify/rotate, etc. the surface:



NB: You might have to active dynamic evaluation of the cells in order to manipulate the surface.

Torus moduli and fractional linear transformations

In the following you can play with the equivalence of tori whose modular parameters, τ, are related by T and S transformations. If you download the notebooks and run them in Mathematica, you can play with different values for τ.


Here you can see why tori whose modular parameters, τ, are related by T transformations, τ → τ + 1, are equivalent.




Here you can see why tori whose modular parameters are related by an S transformation, τ → -1/τ, are conformally equivalent.