2002 Fiscal Year Final Research Report Summary
Research of the Stable Homoyopy Theory from a view point of KTheory
Project/Area Number 
12640067

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Geometry

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

CoInvestigator(Kenkyūbuntansha) 
SHIMOMURA Katsumi Kochi University, Science, Professor, 理学部, 教授 (30206247)
MINAMI Norihiko Nagoya Institute of Technology, Technology, Professor, 工学部, 教授 (80166090)

Project Period (FY) 
2000 – 2002

Keywords  Real KTheory / Complex KTheory / KLocalizatlon Theory / KOHomology Equivalence / Adams Operation / CwComplex / CwSpectrum / Bousfield's Category 
Research Abstract 
The head investigator introduced the concept of "quasi KO_*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 and the K_*localization. He has already obtained some satisfactory results, and moreover obtained three new results mentioned below during the period of Scientific Research Project in 20002002. The first subject is to classify CWcomplexes (or CWspectra) X by the quasi KO_*equivalence when KU_*X has a simple form such as a free abelian group, a direct sum of a free abelian group and a 2cyclic group and so on. In 2000 he established the classification when KU_*X is isomorphic to the direct sum of two cyclic 2torsion groups 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 an algebraic method enploying the Bousfield's category different from the previous geometrical one constructing small cells complexes. The second subject is to classify Cwcomplexes (or CWspectra) X by the K_*localization when once X has been classified by the quasi KO_*equivalence. For our purpose it is necessary to investigate the behaviour of the Adams operation on KO_*X. However it is never easy to determine their K_*local types because the behaviour of the Adams operation on KO_*X is very complicated. In 20012002 he determined the K_*local type of X when KU_*X is isomorphic to the free abelian group of rank 2 or the direct sum of the free abelian group of rank 1 and a 2cyclic group.

Research Products
(15 results)