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The topology of alternating knots
Student-Run Geometry/Topology| Speaker: | Alexander Coward, UC Davis |
| Location: | 1147 MSB |
| Start time: | Tue, Feb 8 2011, 12:10PM |
Description
If you follow a knot diagram around the curve of the knot,
oftentimes the crossings are arranged over, under, over, under, over,
under, etc... Such a diagram is called an alternating diagram, and
knots which admit an alternating diagram are called alternating knots.
In this talk we will prove some of the remarkable properties of
alternating knots, such as:
- An alternating diagram of a knot minimizes crossing number of a knot.
- An alternating diagram of a link is split it and only if the link is split.
- Crossing number of alternating knots is additive under knot connect sum.