Crossing numbers of composite knots and spatial graphs

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• Benjamin Bode, Osaka
• Monday 23 November 2020, 14:00-15:00
• https://bham-ac-uk.zoom.us/j/86949010415.

If you have a question about this talk, please contact Johannes Carmesin.

The crossing number of a knot K is the minimal number of crossings in any knot diagram representing K. Despite this straightforward definition and its historical significance computing the crossing number of a knot is a big challenge, since there is no general procedure to decide whether a given diagram is minimal. In this talk I am going to discuss the question whether the crossing number is additive under the connected sum operation, a conjecture that remains open after more than 100 years. After a brief general introduction to the theory of knots and spatial graphs I will prove results about the crossing numbers of certain spatial graphs and show how these can be related to crossing numbers of knots.

This talk is part of the Study group in Graph Theory, Topology and Algorithms series.

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• https://bham-ac-uk.zoom.us/j/86949010415

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