| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Research Abstract |
Two 3-manifolds are called cobordant if they are realized as the boundary of a smooth 4-manifold. In particular, if it preserves the homology group which is one of the topological invariants of manifolds, then they are called homology cobordant, and their structures reflect the depth of the fundamental group which is also one of the topological invariants. In this research, by using a method called the gauge theory which originates in physics, we gave a necessary condition for several number of 3-manifolds called lens space are the boundary of a certain kind of smooth 4-manifold in terms of representations of the fundamental group of the 4-manifold giving the cobordism. Moreover, we explicitly calculated the topology of the space of all representations in a certain kind of matrices of the fundamental group of the space obtained by removing a knot from the 3-sphere, and determined the structure of a certain part.
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