#17030: Knot Theory as a part of GSoC 2014.
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Reporter: amitjamadagni | Owner: amitjamadagni
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.2
Component: algebraic | Resolution:
topology | Merged in:
Keywords: | Reviewers: Miguel Marco, Karl-
Authors: Amit Jamadagni, | Dieter Crisman, Frédéric Chapoton,
Miguel Marco | Travis Scrimshaw
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/ticket/17030 | 0cce5891b429ea267c45bd89adacff6ebb12e453
Dependencies: | Stopgaps:
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Comment (by tscrim):
Replying to [comment:173 fuglede]:
> Replying to [comment:171 tscrim]:
> > In that case, I agree. Although this doesn't agree with Seifert's
construction AFAIK, and for 4+ components, at least by my understanding of
how you are constructing things, wouldn't give a surface.
>
> I'm not really constructing anything at all, so I'm not quite sure what
it is that would not be a surface.
I thought you were taking '''S'''^1^ x '''S'''^1^ and then connecting up
points inbetween. Now that I actually drew something, you were taking the
two unknots and drawing them projected into the plane with overlap, where
I did get a cylinder.
> > In that case the `2 -2` are canceled automatically by the braid group:
> > {{{
> > sage: B = BraidGroup(4)
> > sage: B([1,2,-2])
> > s0
> > }}}
>
> Yeah, that makes sense. Isn't it a bit unfortunate that one would need
to understand the `BraidGroup` internals in order to use the knot theory
module, though? If I just read the documentation in `Link`, then I might
assume that `[1, -2, -2]` contains knots on all three strands (that's what
I did anyway).
I agree. Do you think a warning with an example would be sufficient (if
it's not possible to quickly fix) to clarify things?
> > PS - I agree, "disjoint" is not a good word. Perhaps "separable" is a
better?
>
> Yes, I believe I've heard "separable" being used in this context as
well, although I can't seem to find a written source at the moment. The
word of course already has another meaning in the context of topological
spaces, but that's not really an issue. In any case, you could always just
go with "bounds and oriented disconnected surface".
True.
--
Ticket URL: <http://trac.sagemath.org/ticket/17030#comment:174>
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