Researcher Database

（Last updated : 2020-09-29 17:36:03）

FUKUMOTO Yoshihiro

Department / Course College of Science and Engineering Department of Mathematical Sciences

Title / Position Professor

Other Affiliations
1.	Graduate School of Science and Engineering

Academic background
1.	1999/03 Degree Acquisition	│ Kyushu University Doctor (Mathematics)
2.	1995/03 Degree Acquisition	│ Kyushu University Master (Mathematics)
3.	～1995/03	Master Course │ Graduate school of Mathematics │ Kyushu University │ Completed
4.	～1999/03	Doctoral Program (2nd Semester) │ Graduate school of Mathematics │ Kyushu University │ Completed

Business career
1.	2012/09 ～ 2013/09	Visiting Scholar │ │ Indiana University ,

Subject of research
1.	Cobordism category of 3-manifolds and analysis on moduli spaces of flat connections
2.	Higher Dimension of Bounding Genus and Application of Its Higher Dimension Manifold to Cobordism Category
3.	Elucidation of Structures of Cobordism Category Homology Cobordism Monoid of 3-manifolds
4.	Elucidation of Structure of Bounding Genus and Its Elaboration

Research summary
Cobordism category of 3-manifolds and analysis on moduli spaces of flat connections As topological quantum field theories in the (3+1) dimension develop, the structure of rational homology cobordism group constituted by the entire rational homology 3-sphere has yielded a lot of results using homology cobordism invariants, such as K. Froyshov's h-invariants and P. Ozsvath-Z. Szabo's d-invariants. On the other hand, it is our forthcoming challenge to characterize cobordism that describes the time evolution of a system. This research intends to identify the structure of cobordism category that corresponds to refinement with cobordism considered as morphism, by applying gage theory, with focus on the two points as follows: 1) Instantons on 4-manifolds with tubular edges, and Chern-Simons invariants on 3-manifolds 2) Indicating manifold of 3-manifolds and structure of edges in the instanton/muduli space

Present specialized field
Geometry, Global Analysis (Keyword：gauge theory, homology cobordism group, instantons, moduli spaces, flat connections, lens spaces, knots, character variety)

Papers
1.	2016	Traceless SU(2) representations of 2-stranded tangles │ Mathematical Proceedings of the Cambridge Philosophical Society │ (Co-authored)
2.	2011/10	w-Invariants and the Fintushel-Stern Invariants for Plumbed Homology 3-Spheres │ Experiment. Math. │ 20 (1),pp.1-14 (Sole-authored)
3.	2010	Bounding Genus and the Spin Cobordism Category of 3-manifolds │ INTERNATIONAL CONGRESS OF MATHEMATICIANS Hyderabad 2010 ABSTRACTS Short Communications │ ,pp.159-160 (Sole-authored)
4.	2009	The bounding genera and w-invariants │ Proc. Amer. Math. Soc. │ 137,pp.1509-1517 (Sole-authored)
5.	2009	Cobordism category of plumbed 3-manifolds and intersection product structures │ Journal of Homotopy and Related Structures │ Vol.4 (No. 1),pp.39-68 (Sole-authored)
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Academic conference presentation
1.	2010/08/22	Bounding Genus and the Spin Cobordism Category of 3-manifolds (INTERNATIONAL CONGRESS OF MATHEMATICIANS Hyderabad 2010)