Construction of 4-manifolds related to exceptional surgeries on 3-manifolds

2016 Fiscal Year Final Research Report

• Project/Area Number: 24540070
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: The University of Electro-Communications
• Principal Investigator: YAMADA YUICHI 電気通信大学, 大学院情報理工学研究科, 教授 (30303019)
• Co-Investigator(Renkei-kenkyūsha): TANGE MOTOO 筑波大学, 数理物質系, 助教 (70452422) ; ABE TETSUYA 大阪市立大学, 数学研究所, 特任准教授 (00614009)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 多様体 / ４次元多様体 / ３次元多様体 / デーン手術 / レンズ空間 / 枠付き絡み目 / カービー計算

Outline of Final Research Achievements

Phenomenon that a Dehn surgery along a hyperbolic knot in the 3-sphere yields a non-hyperbolic manifold is called "exceptional surgery" and is a subject in the topology of low-dimensional manifolds. We are interested in construction of curious 4-manifold of great interest, related to exceptional surgeries. Results are: (1) Study on pairs of distinct knots that yield the same lens spaces. (2) Study on exceptional Dehn surgeries along the Mazur link, and its generalization, from the view point of "geography". (3) Held a workshop "Differential Topology 17", on Heegaard Floer holmology. Here, Heegaard Floer (HF) is a new theory, appeared and quickly developed in 2000-2010.

Free Research Field

数物系科学