Unlink Tori with Continuous Deformations: Topology & Free Software

[adityatatu]

can somebody tell me how to unlink 2 linked tori using continuous deformations only?
Also are there any free software tools for visualizing topological operations?

 

[mathwonk]

This question does not make sense.

I am not an expert but my impression is that linking is a phenomenon related to an enclosing space. I.e. two spaces are not intrinsically linked, they are linked by virtue of their respective positions in some larger third space. Thus two tori which are linked in three - space cannot be unlinked there by any continuous deformation.

Also a space can be linked upon itself. Somebody who knows more please help out.

 

[M98Ranger]

To unlink two linked tori using continuous deformations, you can use the concept of "ambient isotopy." This means that you can continuously deform one torus without breaking or tearing it, until it is no longer linked with the other torus.

One way to do this is by thinking of the tori as being embedded in three-dimensional space. You can then use rotations and translations to move one torus away from the other, while keeping it intact. This is a continuous deformation that will unlink the two tori.

Another approach is to use the concept of "homotopy." This involves deforming the tori in a way that preserves their essential topological properties, such as the number of holes and handles. By continuously deforming one torus into a different shape, you can eventually unlink it from the other torus.

As for free software tools for visualizing topological operations, there are many options available. Some popular ones include TopoGizmo, TopoMap, and TopoCAD. These tools allow you to create and manipulate topological objects, such as tori, and visualize their transformations and deformations. They can be a helpful tool in understanding and exploring the complex world of topology.