| 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)
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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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