| Project/Area Number |
60460001
|
|---|
| Research Category |
Grant-in-Aid for General Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
代数学・幾何学
|
|---|
| Research Institution | HOKKAIDO UNIVERSITY |
|---|
Principal Investigator |
SUZUKI Haruo DEPARTMENT OF MATHEMATICS, HOKKAIDO UNIVERSITY Prof., 理学部, 教授 (80000735)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
HIAI Fumio RESEARCH INSTITUTE OF APPLIED ELECTRICITY, HOKKAIDO UNIVERSITY Associate Prof., 応用電気研究所, 助教授 (30092571)
IZUMIYA Shiyuici DEPARTMENT OF MATHEMATICS, HOKKAIDO UNIVERSITY Associate Prof., 理学部, 助教授 (80127422)
MORIMOTO Tohru DEPARTMENT OF MATHEMATICS, HOKKAIDO UNIVERSITY Associate Prof., 理学部, 助教授 (80025460)
KAMISHIMA Yoshinobu DEPARTMENT OF MATHEMATICS, HOKKAIDO UNIVERSITY Lecturer, 理学部, 講師 (10125304)
NISHIMORI Toshiyuki DEPARTMENT OF MATHEMATICS, HOKKAIDO UNIVERSITY Associate Prof., 理学部, 助教授 (50004487)
|
|---|
| Project Period (FY) |
1985 – 1986
|
| Project Status |
Completed (Fiscal Year 1986)
|
| Budget Amount *help |
¥5,700,000 (Direct Cost: ¥5,700,000)
Fiscal Year 1986: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1985: ¥3,400,000 (Direct Cost: ¥3,400,000)
|
|---|
| Keywords | Manifold / Foliation / Characteristic Class / Group Action / Lie Algebra / Singular Point / 作用素環 |
|---|
| Research Abstract |
THE PURPOSE OF THE PROJECT WAS TO INVESTIGATE GLOBAL PROPERTIES OF MANIFOLDS FROM VIEWPOINTS OF TOPOLOGY, DIFFERENTIAL GEOMETRY AND ANALYSIS. CONTENTS OF RESULTS IN THE PROJECT ARE SUMMARIZED AS FOLLOWS:
1. COHOMOLOGY CLASSES OF A FOLIATION HOLONOMY GROUPOID, CORRESPONDING TO WEIL OPERATORS ARE CONSTRUCTED. THESE ARE REGARDED AS GENERALIZATIONS OF THE MODULAR CLASS CORRESPONDING TO THE TRANSVERSE MEASURE OF THE HOLONOMY GROUPOID. THESE COHOMOLOGY CLASSES ARE CLOSELY RELATED TO THE STRUCTURE OF A FOLIATION OPERATOR ALGEBRA. THE NOTION OF AVERAGE SIGNATURE O OF A 4n-DIMENSIONAL NON-COMPACT MANIFOLD IS INTRODUCED. PROPERTIES OF A COMPACT CONFORMALLY FLAT MANIFOLD OF DIMENSION <>!=> 3 WHOSE DEVELOPING MAP IS NOT SURJECTIVE, IS CLEARIFIED.
2. A TRANSITIVE FILTERED LIE ALGEBRA WITH DEPTH <mu> IS DEFINED AND A STRUCTURE THEOREM FOR IT IS PROVED. IT IS SHOWN THAT THE GENERIC SINGULARITIES OF AN ENVELOPE AND THE GENERIC LEGENDRE SINGULARITIES ARE EQUIVALENT. PARITY OF THE NUMBERS OF INFLEXION POINTS AND THOSE OF VERTICES OF A GENERIC CURVE IN A 2-DIMENSIONAL MANIFOLD ARE DETERMINED.
3. RELATIONS BETWEEN A MAJORIZATION IN A NON-COMMUTATIVE MEASURE SPACE, CONSISTING OF A SEMEI-FINITE VON NEUMANN ALGEBRA AND A NORMAL SEMI-FINITE TRACE, AND A DOUBLE STOCHASTIC MAP ARE CLEARIFIED. AN EXTENSION THEOREM FOR A NON-LINEAR COMPLETE POSITIVE MAP DEFINED ON A SUBALGEBRA OF A <c"*> -ALGEBRA IS OBTAINED.
|
