Deepening singularity theory and low dimensional geometry

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400087
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kobe University
• Principal Investigator: Saji Kentaro 神戸大学, 理学研究科, 准教授 (70451432)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 特異点 / カスプ辺 / 接触構造 / 曲率

Outline of Final Research Achievements

For deepening singularity theory, I obtained criteria for Morin singularities for the case of the dimension of the source space and the target space is not the same. By using criteria for Morin singularities, I gave the number of right-left isotopy classes.
For low dimensional geometry, I generalized a formula for the number of singular points and the Euler characteristic to singularities of bundle homomorphisms. I also gave a normal form by only using isometric coordinate transformation of the target space for cuspidal edges and swallowtails. Moreover, I clarified the differential geometric meanings for modulus appeared in the lower degree terms. By using that form, I obtained generic configurations of asymptotic lines and characteristic lines of that singularities. I also studied singularities of solution surfaces of certain differential equation and that of surfaces which approximate the cuspidal edge.

Free Research Field

微分トポロジー