Project/Area Number  09640103 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Geometry

Research Institution  Nagoya Institute of Technology 
Principal Investigator 
YOSHIMURA Zenichi Nagoya Institute of Technology, Technology, Professor, 工学部, 教授 (70047330)

CoInvestigator(Kenkyūbuntansha) 
山岸 正和 名古屋工業大学, 工学部, 講師 (40270996)
SAEKI Akihiro Nagoya Institute of Technology, Technology, Lecturer, 工学部, 講師 (50270997)
OHYAMA Yoshiyuki Nagoya Institute of Technology, Technology, Assist.Prof., 工学部, 助教授 (80223981)
上野 一男 名古屋工業大学, 工学部, 助教授 (10193822)
ADACHI Tosiaki Nagoya Institute of Technology, Technology, Assist.Prof., 工学部, 助教授 (60191855)
MINAMI Norihiko Nagoya Institute of Technology, Technology, Assist.Prof., 工学部, 助教授 (80166090)
NATSUME Toshikazu Nagoya Institute of Technology, Technology, Professor, 工学部, 教授 (00125890)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥2,000,000 (Direct Cost : ¥2,000,000)
Fiscal Year 1998 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1997 : ¥1,200,000 (Direct Cost : ¥1,200,000)

Keywords  Real KTheory / Complex KTheory / KLocalization Theory / KOHomology Equivalence / Mod 8 Lens Space / CWSpetrum / Weighted Projective Space / Thom Complex / 実K理論 / 複素K理論 / K局所化理論 / KOホモロジー同値 / 法8レンズ空間 / 荷重複素射影空間 / CWスペクトラム / Thom複体 / 実射影空間 / レンズ空間 / アダムス作用素 
Research Abstract 
The head investigator introduced the concept of "quasi K0*equivalence" in 1990, in order to give a certain classification of CWcomplexes or manifolds, which is weaker than the classification based on the K localization. Since then, he has continued to research mainly the following two subjects concerned with the quasi KO_*equivalence. He has already obtained some satisfactory results, and moreover obtained two new results mentioned below during the period of Scientific Research Project in 1997 1998. The first subject is to classify CWcomplexes (or CWspectra) X by the quasi KO_*equivalence when KU_<xxxxx>*X has a simple form. In 1997 he established the classification when KU_*X is isomorphic to the direct sum of a free abelian group and one cyclic 2torsion group without the assumption that KU_1X 0. Although there is an obstruction to establish our classification unless KU_1X = 0, he succeeded to overcome its obstruction by considering a pair of X and its dual DX simultaneously. The second subject is to determine the quasi K0_*equivalent types of some known manifolds (or CWcomplexes). In 1998 he determined the quasi KO_*equivalent types of the stunted mod 8 lens spaces L_n/L_m as a joint work with Y.Nishimura(Osaka City Univ.). It is very bothersome to determine their quasi K0_*equivalent types in the usual way because the behavior of the conjugations on KU_*L_n/L_mis very complicated. To avoid a wasted effort he investigated several basic properties about the quasi K0_*equivalent types of stunted mod q lens spaces by using Thorn complexes and weighted projective spaces. Consequently he suceeded to limit the investigation of the conjugations to a minimum.
