#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):
I see what the problem is now (after treating enough symptoms). In
Definition 2.11, there is this: "For a link with a disconnected Seifert
surface we define the Alexander polynomial to be zero." So we just need to
check to see if the links can be separated, which means the braid
representation can be broken into 2 disjoint components.
However, I believe the Seifert matrix is correct as it encodes the H,,1,,
information of the Seifert surface. Since the unlink is a disjoint union
of 2 disks, the positive homology groups are all trivial, so the Seifert
matrix should be a 0x0 matrix. (If you want to think of it as a [empty]
cylinder, H,,1,, is also trivial in that case as well. However, I don't
think this is the correct construction of the Seifert surface from the
reading I've done, but I'm not an expert.)
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Ticket URL: <http://trac.sagemath.org/ticket/17030#comment:169>
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