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Minimal Genus Seifert surface of 11 crossing alternating knots
Student-Run Research Seminar| Speaker: | Neetal Neel, UC Davis |
| Location: | 3106 Mathematical Science Building |
| Start time: | Wed, Nov 15 2023, 12:10PM |
The Kakimizu complex of knots for crossings less than or equal to 10 has been found by O.Kakimizu in 1992. The 0 skeleton of the Kakimizu complex of 2-bridge links was found by Hatcher and Thurston, generalized by Sakuma to find the Kakimizu complex of Special Arborescent links. Jessica Banks gave a complete proof of results announced by Hirasawa and Sakuma, describing explicitly the Kakimizu Complex of a non-split, prime special alternating links. The Kakimizu complex of prime, non-split alternating links has finite vertices. We find the Kakimizu complex for all $11$ crossing alternating knots. For most links we were able to use the algorithms known to us. We found the rest of the Kakimizu complex using sutured manifold theory. I will give a brief exposition of the algorithms known, for computing the Kakimizu complex of links and future questions.
Free pizzas:)