Contact topology from the view point of round surgery

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400077
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: Adachi Jiro 北海道大学, 理学研究院, 理学研究院研究員 (20374184)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 接触構造 / ラウンド手術

Outline of Final Research Achievements

Contact structure is an important geometric structure, that is related to classical mechanics and optics. Apart from such a historical background, the study of contact structure as a pure geometric structure has been remarkably developed recently from the view point of differential topology.
In this research project, I applied the "round surgery" method to contact manifolds, that was used for other studies. As a result, I extended the studies which had been mainly done on contact structures of the first order on 3-dimensional manifolds to the cases of higher-dimension and higher-order. It is expected that various studies will be developed by using this method.

Free Research Field

微分トポロジー