イベントカレンダー

東京科学大学トポロジーセミナー：佐藤光樹氏

講演タイトル: An unoriented analogue of slice-torus invariant
アブストラクト: 　A slice-torus invariant is an real-valued homomorphism on the knot concordance group whose value gives a lower bound for the 4-genus such that the equality holds for any positive torus knot. Such invariants have been discovered in many of knot homology theories, while it is known that any slice-torus invariant does not factor through the topological concordance group. In this talk, we introduce the notion of "unoriented slice-torus invariant" and show that three invariants derived from knot Floer, Khovanov and instanton Floer homology respectively are unoriented slice-torus invariants. As an application, we give a new method for computing those invariants and determine the values of (-2,p,q)-pretzel knots for any odd p,q>1. Moreover, we use the method to prove that any unoriented slice-torus invariant does not factor through the topological concordance group.

更新日：2024.09.11