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Results tagged with knot-theory
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user 1463
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.
9
votes
Accepted
Relatively hyperbolic knot groups
The following theorem, which can be deduced from a combination theorem of Dahmani, is stated as Theorem 7.2.2 in our book 3-manifold groups .
Theorem: Let $N$ be a compact, orientable, irreducible …
- 25.2k
8
votes
Finite two-relator groups and quotients of knot groups
Question 1:
As mentioned in comments, presentations with the same number of generators and relations are called balanced. The triviality problem for balanced presentations appears to be a question of …
- 25.2k
3
votes
Fundamental group of the complement of a codimension two submanifold
As you suspect, in dimension 3 the answer to your first question should be "no". Indeed, if one deletes any collection of circles from $M$ then the complement is a 3-manifold with toroidal boundary. S …
- 25.2k