Singularity theory of product maps and its applications

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800042
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kyoto University (2016-2017); Kyushu University (2014-2015)
• Principal Investigator: Takao Kazuto 京都大学, スーパーグローバルコース数学系ユニット, 特定助教 (80643832)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 可微分写像 / 特異点 / Stein分解 / 低次元多様体 / Heegaard分解 / 結び目 / 橋位置 / 橋分解

Outline of Final Research Achievements

I worked on a new area in singularity theory of differentiable maps with particular attention to product structures of maps, and on its applications to low-dimensional topology. In consequence, I made steady progress on the stability and deformations of singularities of the product map of multiple functions, which will hopefully base future developments and applications. I also worked on related topics and obtained some unexpected results, including a certain significant discovery on the theory of bridges of knots.

Free Research Field

トポロジー