Project/Area Number  07640081 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Geometry

Research Institution  Hokkaido University 
Principal Investigator 
NISHIMORI Toshiyuki Hokkaido University, Center for Research and Development in Higher Education, Professor, 高等教育機能開発総合センター, 教授 (50004487)

CoInvestigator(Kenkyūbuntansha) 
NAKAI Isao Hokkaido University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90207704)
MINAKAWA Hiroyuki Hokkaido University, Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (30241300)
SUWA Tatsuo Hokkaido University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40109418)

Project Fiscal Year 
1995 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 1996 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1995 : ¥1,300,000 (Direct Cost : ¥1,300,000)

Keywords  foliation / qualitative theory / holomerphic foliation / wob / foliated bundle / similarity pseudogroup / residue / PL homeomorphism group / 葉層構造 / 定性論 / 正則葉層 / 織構造 / 葉層バンドル / 相似変換擬群 / 留数 / PL同相群 / 葉層 / 横断的幾何構造 / 複素葉層 / 同相群 
Research Abstract 
The purpose of this research was to investigate the structures and properties of foliations in a broad sense. Head Investigator T.Nishimori has been studying the qualitative theory of similarity pseudogroups in order to extend the qualitative theory of codimension one foliations for foliations of higher codimension. To prepare a firm base for the trial, he gave a detailed proof for Hector's Uniform Convergence Theorem in an extended form of class C^<1+Lipschitz> category. Investigator T.Suwa extended a theorem of Baum and Bott, connecting the residue of singular holomorphic foliations and their topological invariants, to open manifolds, and extended one of his own theorems to singular varieties of higher dimension. Furthermore, by introducing Nash residue, he gave a partial answer to the rationality Conjecture of Baum and Bott. Invesigator I.Nakai gave a geometric interpretation of the curvature form in terms of fake billiard and proved that a weakly associative nweb is associative if Chern connections of triples of the members are not flat, and then the foliations are defined by members of a pencil (projective linear family of dim 1) of 1forms. This results completed the classification of weakly associative 4webs initiated by Poincare, Mayrhofer and Reidemeister for the flat case. Investigator H.Minakawa constructed exceptional homomorphisms of the fundamental group of a closed orientable surface to the diffeomorphism group of a circle whose Euler class satisfies the equality bounding Ghys Inequality (arising from MilnorWood Inequality). Furthermore he classified exotic circles in the piecewise liniear homeomorphism group of a circle.
