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Results tagged with knot-theory
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user 8899
Knot theory is dealing with embedding of curves in manifolds of dimension 3. A knot is a single circle embedded in the affine space of dimension 3 as a smooth curve not crossing itself. Many knot invariants are known and can be used to distinguish knots.
17
votes
Accepted
Propagation of an error in the LMO invariant? (Revision: I don't think LMO is wrong!)
Having been a part of the LMO story from its beginning, and having read and checked all relevant papers carefully at the time, and having taken part in many cross-checks that the LMO invariant passed …
- 1,960
13
votes
1
answer
696
views
Integer matrices with a strange divisibility property
Fix an integer $n$. What can you say about a (not necessarily square) matrix $A$ with integer entries that has the property that for any $k$, every $k\times k$ minor of $A$ is divisible by $n^{k-1}$? …
- 1,960
35
votes
Is there a "knot theory" for graphs?
The theory of knotted trees is obviously trivial. So given a knotted graph $\Gamma$, take a maximal tree in it and you can bring it to a standard form, say to be embedded as a planar object inside a t …
- 1,960