An Invitation to Knot Theory: Virtual and Classical by Heather A. Dye

Author:Heather A. Dye
Language: eng
Format: epub, azw3
Publisher: Taylor & Francis Group, LLC
Published: 2016-03-07T16:00:00+00:00

Find a simple method of determining the virtual genus of a virtual link. It is easy to find an upper bound on the virtual genus of a link, but much more challenging to find the virtual genus and prove that it is minimal.

Projects

Practice visualizing surface link pairs.

Construct a sequence of surface link pairs that prove that virtual crossing number is not bounded by the virtual genus.

Construct a sequence of virtual links that have virtual crossing number n and virtual genus n. (Do not try to prove that the virtual genus is n.)

Consider families of virtual pretzel knots (in tangle notation: w1, w2, . . . wn). Give a conjecture about their virtual genus with supporting examples.

Construct a family of rational knots and give a conjecture about their virtual genus. Support your conjecture with examples.

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