Innovative research of geometric topology and singularities of differentiable mappings

KAKEN

About this project

Japan Grant Number
JP17H06128
Funding Program
Grants-in-Aid for Scientific Research
Funding organization
Japan Society for the Promotion of Science
Project/Area Number
17H06128
Research Category
Grant-in-Aid for Scientific Research (S)
Allocation Type
  • Single-year Grants
Review Section / Research Field
  • Science and Engineering > Mathematics and Physics > Mathematics > Geometry
Research Institution
  • Kyushu University
Project Period (FY)
2017-05-31 〜 2022-03-31
Project Status
Completed
Budget Amount*help
81,640,000 Yen (Direct Cost: 62,800,000 Yen Indirect Cost: 18,840,000 Yen)

Research Abstract

We established a global and concrete simplification method for differentiable maps using geometric topology and discovered that 4-dimensional manifolds always have good structures. We also formulated for the first time the cobordism of maps of manifolds with boundary, which is significant for creating a new research area. Furthermore, we found that nonsingular fibers and singular sets are sometimes not linked, and our application of this discovery to the theory of submersions is a remarkable example of the versatility of the singularity theory. We have also reformulated the theory of dual flat structures, which is important in information geometry, so that it can be applied to singular models as well, and has promoted the construction of next-generation catastrophe theory for applications in various scientific fields.

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