1998 Fiscal Year Final Research Report Summary
On the construction and classification of the finite geometry
Project/Area Number 
09640306

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
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. > 福岡大学, 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 Period (FY) 
1997 – 1998

Keywords  geometry / homotopy / algebra / cohomology / plane / Schur ring 
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).

Research Products
(14 results)