Research on distances of Heegaard splittings of 3-manifolds and bridge splittings of links

2014 Fiscal Year Final Research Report

• Project/Area Number: 25887039
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Nara Women's University
• Principal Investigator: JANG Yeonhee 奈良女子大学, 自然科学系, 助教 (90708348)
• Project Period (FY): 2013-08-30 – 2015-03-31
• Keywords: へガード分解 / 絡み目の橋分解 / ヘンペル距離

Outline of Final Research Achievements

We proved that, for any integer n greater than 1, there exist Heegaard splittings of 3-manifolds and bridge splittings of links whose Hempel distance is exactly n. Moreover, we showed the existence of Heegaard splittings for which there is a unique pair of disks realizing the distance. Also, we focused on the fact that relationship between bridge splittings of a knot can be described by a graph, and showed that a new type of graph can describe such relationship of a certain knot, which is an interesting example admitting bridge splittings that are locally minimal but not globally minimal.

Free Research Field

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