Knot On Dogs Head Sep 18 2025 nbsp 0183 32 The complement of the open solid torus is known as a knot exterior The homotopy equivalence between knot exteriors and knot complements is an important observation in basic
Oct 20 2011 nbsp 0183 32 See also the blog post How can I draw a knot in TeX I need to use TikZ to draw some knot braid diagrams These will be built from families of curves which appear to cross Sep 8 2015 nbsp 0183 32 But if the knot is not the crossings locally can be perturbed slightly to lie in a quot slice quot of mathbb R 3 where the argument holds Usually this is thought of as making your knot in
Knot On Dogs Head
Knot On Dogs Head
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May 2 2011 nbsp 0183 32 I was wondering if anyone could suggest software packages to create nice knot diagrams hopefully with a link to images they have made in the past I have used xy pic Jun 20 2017 nbsp 0183 32 Since knot groups are infinite the linear representation theory tends to be rather complicated however One application of representations of a knot group is to twist the chain
May 9 2021 nbsp 0183 32 A knot being slice means that it does and is non slice if it does not In particular Lisa Piccirillo showed that the Conway knot is not slice so does not bound a nicely embedded Oct 24 2024 nbsp 0183 32 I have the difficulty to understand the knot group of the 2 component link in mathbb R 3 especially it is not commutitive Let l l 1 cup l 2 be the union of two
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Repeating knots is the usual approach If you repeat control vertices you ll get a curve that has zero derivative vectors of several orders at the end points which will cause problems It will May 19 2014 nbsp 0183 32 It is well known that the first homology group of a knot complement mathbb R setminus K is isomorphic to the integers mathbb Z which can also be computed
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