Research on 3-manifolds and links based on the Heegaard theory

2022 Fiscal Year Final Research Report

• Project/Area Number: 21K20328
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: Nara Women's University
• Principal Investigator: Jang Yeonhee 奈良女子大学, 自然科学系, 准教授 (90708348)
• Project Period (FY): 2021-08-30 – 2023-03-31
• Keywords: へガード分解 / 橋分解 / Hempel距離

Outline of Final Research Achievements

As a result of research on Hempel distance for Heegaard splittings of 3-manifolds and bridge splittings of links, we proved that there exist a lot of keen and strongly keen bridge splittings of links.
It seems that the concept of bridge splittings of links were defined in several different way and have been treated as the same concept so far, but we tried to make it clear the differences between them. As a result, we obtain a certain results on relations among homeomorphism classes and isotopy classees of bridge decompositions and isotopy classes of bridge positions.

Free Research Field

位相幾何学

Academic Significance and Societal Importance of the Research Achievements

これまで同様な概念として扱われてきた概念の間に一部本質的な違いがあることも含めて、それらの関係が明らかになったのは、今後の橋分解の研究に大きな影響を与えると考える。また、keenおよびstrongly keenな橋分解は分解のGoeritz群の有限性との関係等、様々な良い性質を持っていると思われることから、橋分解と関係する多方向への研究に貢献できるのではないかと期待している。