A research on assembly maps in algebraic L-theory
| Project/Area Number |
20540100
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Okayama University of Science |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2008 – 2011
|
| Project Status |
Completed (Fiscal Year 2011)
|
| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
|
|---|
| Keywords | 代数的L理論 / アセンブリ写像 / ホモロジー / 指数 / アセンブリ / 手術完全列 |
|---|
| Research Abstract |
I proved that the assembly map from the homology groups of a space X with algebraic L-theory spectral sheaf coefficient to the L-groups splits through controlled L-groups, when the control map is simplicially stratified. When we consider the L-theory of-infinity version, then the controlled assembly maps from the homology groups to the controlled L-groups are isomorphisms. The key ingredient is a squeezing structure for L-theory cycles. I also extended the classical Poincare-Hopf theorem on vector fields on manifolds to the case when there are singularities on the boundary, by introducing several new type of indices.
|
Report
(6 results)
Research Products
(13 results)
