Topology, contact geometry, and fundamental group of 3-manifolds from open book decomposition

2014 Fiscal Year Final Research Report

• Project/Area Number: 25887030
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: ITO Tetsuya 京都大学, 数理解析研究所, 助教 (00710790)
• Project Period (FY): 2013-08-30 – 2015-03-31
• Keywords: 三次元多様体 / 接触幾何 / 組みひも群

Outline of Final Research Achievements

A contact 3-manifold is presented by using the mapping class group by using an open book decomposition. By using open book decomposition we develop a method to study contact 3-manifolds in more topological way. As products, we showed that an overtwisted disc can be put in a good position so that it essentially intersects with pages of open books, and obtain a generalization of Jones' conjecture concerning the algebraic linking number and braid indices.

Free Research Field

低次元トポロジー