Project/Area Number  09640306 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Fukuoka University 
Principal Investigator 
ODA Nobuyuki Fukuoka Univ., Fac.of Science, Prof., 理学部, 教授 (80112283)

CoInvestigator(Kenkyūbuntansha) 
AKIYAMA Kenji Fukuoka Univ., Fac.of Science, Prof., 理学部, 教授 (70078575)
AKITA Toshiyuki Fukuoka Univ., Fac.of Science, Assistant, 理学部, 助手 (30279252)
KUROSE Takashi Fukuoka Univ., Fac.of Science, Assoc.Prof., 理学部, 助教授 (30215107)
INOUE Atsushi Fukuoka Univ., Fac.of Science, Prof., 理学部, 教授 (50078557)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,800,000 (Direct Cost : ¥1,800,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1997 : ¥1,000,000 (Direct Cost : ¥1,000,000)

Keywords  geometry / homotopy / algebra / cohomology / plane / Schur ring / 幾何 / ホモトピー / 代数 / コホモロジー / 平面 / シュアー環 / 射影平面 / 共線変換群 / 擬正則 / 積差集合 
Research Abstract 
Geometrical constructions in homotopy sets were studied. We obtained results on the GAMMAWhitehead product and the GAMMAHopf construction. We introduced the transformation between pairings and copairings and showed its applications. We obtained a formula for the smash product. We obtained a generalization of the HardieJansen product and studied its properties. Dual results are also studied. For geometrical construction in operator algebras, TomitaTakesaki theory was studied. We obtained results on unbounded C^*seminorms on *algebra and standard weights which enable us to develop unbounded TomitaTakesaki theory. We constructed explicit examples of surfaces in affine spaces of dimension three and four. We gave a necessary and sufficient condition on surfaces in a threedimensional affine space to be metric when the surfaces have nonzero constant GaussKronecker curvature. The cohomology of mapping class groups was studied. We obtained a relation among periodic automorphisms of closed surfaces and the etainvariant of their mapping tori. We also obtained various vanishing theorems of mod 2 MoritaMumford classes. The Schur ring of product type was characterized by the existence of a subgroup of a collineation group. The existence of a Schur ring of produt difference set type is characterized by a finite projective plane of order n with a collineation group of order n(n  1).
