Contraction in singular heights

[davidreutter]

I think whenever one performs a sidewards click and drag operation in a singular height, homotopy.io should first iterate through the slice (from 'top' to 'bottom') and see whether it can perform a contraction operation before expanding that height. For example, in the worksheet attached below, clicking and dragging the singularity to the left results in an expansion of the singular height where one would rather expect a contraction of the 'bottom-most' wire to the right. I cannot think of a case where one would rather perform an expansion instead of a contraction at a singular height. Of course, expansions can still be performed by operating one projection below.

https://homotopy.io/#$proof=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

[jamievicary]

I agree with this.

I'm not sure I agree with the terminology however - these are all expansions. These come in "factoring" and "bubbling" forms. I interpret your point as saying that factoring expansions are always more desirable than bubbling ones, where they are possible, and I agree.

These bubbling expansions are at times critical, for example for doing a Reidemeister 2 move from the identity to 2 braids.

[jamievicary]

I now disagree with my earlier self. Performing a Reidemeister II moves requires performing an expansion at a singular slice. David, what do you think?