Coordinates: | JH Michell Theatre in the Richard Berry Building |

Speaker: |
Joel Hass (UC Davis) |

Title: |
Level n normal surfaces |

Abstract: |
(Joint work with Alex Coward.)
Level n normal surface theory is a variation of the standard theory that has some useful features. 1. Many arguments are conceptually simpler in this setting. 2. It allows for the advantages of 0-efficient triangulations, but without changing the original triangulation. 3. It is set up to efficiently construct iterated normal surfaces, as in the construction of normal hierarchies. In this talk I will introduce these ideas by showing how this theory simplifies the construction of an UNKNOTTING algorithm, and a proof that UNKNOTTING is NP. We can establish these results without using Schubert's Lemma, geometric sums, or the case by case arguments needed in the standard proof. |