Contort rectangle to torus minus splice=homomorphism?

[aheight]

I understand the transformation in general is not homomorphic but what about the transformation minus the splices, that is, contort it all the way up to and not including splicing the edges? Isn't that a homomorphism? Can't we define a bijective function (rotation matrices) to map the two spaces? Seems also to be diffeomorphism as well or no?

 

[fresh_42]

I understand the transformation in general is not homomorphic but what about the transformation minus the splices, that is, contort it all the way up to and not including splicing the edges? Isn't that a homomorphism? Can't we define a bijective function (rotation matrices) to map the two spaces? Seems also to be diffeomorphism as well or no?

If you don't clue the edges, then it is only a "bending", which is both, homeomorph and diffeomorph (as long as you don't fold it somewhere).

 

[math771]

It is not clear what transformation you are referring to, so it is difficult to answer your question accurately. However, in general, a homomorphism is a structure-preserving map between two mathematical objects. It is not clear how rotating matrices would fit into this definition. Additionally, a diffeomorphism is a smooth, bijective map between two differentiable manifolds. Again, it is not clear how this would relate to the transformation you mentioned. Can you provide more context or clarify your question?