2011 Fiscal Year Final Research Report
A research on assembly maps in algebraic L-theory
| Project/Area Number |
20540100
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Okayama University of Science |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Keywords | 代数的L理論 / アセンブリ写像 |
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| 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.
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