Topics from today's class:
- Unknotting number
- k-equivalent knots
- 3.1, 3.3, 3.5, 3.6, 3.7, 3.8c,
Read for next class:
Write one sentence about the reading assignment. You cannot repeat what another student has posted.
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Is the crossing number of a composite knot always the sum of the crossing numbers of the factor knots and do all factor knots need to be reduced for this to be true?
Could the crossing number of a composite knot ever be less than the sum of the crossing numbers of its factor knots?
Is an "easily removed" crossing really well defined? It seems like you could hide them somehow without seriously changing the knot.
I was a little confused about the composite knots and when you can just add the crossing numbers of the components to determine the crossing number and when you cant.
What if we see the knots in 3D spaces. In 3D, some crossing are not "crossed" any more, will that affect the crossing number as a property of the knots?