2024年度
2025/1/8 (Wed.) 16:00-17:00 (H213)
Akihiro Higashitani（東谷 章弘）氏, Osaka University (大阪大学)
Title: Classification of generalized Alexander quandles (in English)
Abstract:
The aim of this talk is to provide a new characterization of isomorphism classes of generalized Alexander quandles in terms of the underlying groups and their automorphisms. This extends the previous result by Higashitani-Kurihara (2024). Additionally, we compute the number of generalized Alexander quandles up to quandle isomorphism arising from groups up to order 127 and their group automorphisms.
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2024/12/20 (Fri.) 16:00-17:00 (H201)
Noboru Ogawa (小川 竜) 氏, Tokai University (東海大学)
Title: Contact contractions and Liouville domains
Abstract:
A Liouville domain is one of the most fundamental objects in symplectic and contact geometry, such as cotangent bundles, affine varieties, etc. Recently, Huang constructed dynamically interesting Liouville domains by using contactly contracting maps. Inspired by Huang's work, we introduce the notion of "compressibility" for contact manifolds and explore their properties. In this talk, after explaining some basics, we show the tightness of compressible contact manifolds and discuss applications to contact Morse theory. Moreover, we present concrete examples of Liouville domains with wild attractors. This talk is based on a joint work with Toru Yoshiyasu.
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2024/10/18 (Fri.) 16:00-17:00 (H201)
Kouki Sato (佐藤 光樹) 氏, Meijo University (名城大学)
Title: An unoriented analogue of slice-torus invariant
Abstract:
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.