Support for parsing d-diagrams to correspond to Manifold object.

3-manifolds / Spherogram

Spherogram is a Python module for dealing with the kind of planar diagrams that arise in 3-dimensional topology, such as link and Heegaard diagrams. It a component of the larger SnapPy project.

https://snappy.math.uic.edu/spherogram.html

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Support for parsing d-diagrams to correspond to Manifold object. #5

Open zitterbewegung opened 4 years ago

zitterbewegung commented 4 years ago

Would it be useful / desirable for snappy to allow for an input of a d-diagram as a text input and then constructing the knot that would represent it? For example

(([[))]] -> Would correspond to a Manifold object of the Trefoil.

More details below.

Manturov, V.O.(2002), Knots and the Bracket Calculus, Acta Applicandae Mathematicae, 74, (3), pp. 293–336.

https://www.researchgate.net/profile/Vassily_Manturov/publication/227058309_Knots_and_the_Bracket_Calculus/links/540d56510cf2f2b29a3839bf/Knots-and-the-Bracket-Calculus.pdf

NathanDunfield commented 4 years ago

What are advantages of this scheme? I am not familiar with it and it's not exactly human readable.

zitterbewegung commented 4 years ago

I agree with you that the notation is unreadable.I was writing a parser for the d-diagram already and I was wondering if it would be useful to contribute back to the Spherogram project. If it is undesirable I will just create my own project for it instead.

From what is in the paper you could

construct a knot based on a finite alphabet.
also the link recognition problem is reduced to a recognition problem in this semigroup.

NathanDunfield commented 4 years ago

Very sorry for the slow response, initially I suggest you do this as a separate project.

zitterbewegung commented 4 years ago

Yea I understood that thanks Z

Sent from my iPhone

On Aug 21, 2020, at 5:35 PM, Nathan Dunfield notifications@github.com wrote:

Very sorry for the slow response, initially I suggest you do this as a separate project.

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culler commented 4 years ago

A suggestion: a function which accepts a d-diagram as input and outputs a PD code for a link projection would be something that anyone who wants to work with d-diagrams could use, in many contexts.

Marc

On Fri, Aug 21, 2020 at 5:35 PM Nathan Dunfield notifications@github.com wrote:

Very sorry for the slow response, initially I suggest you do this as a separate project.

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