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10/8-inequality and plumbed rational homology 3-spheres
- Speaker(s)
- Yoshihiro Fukumoto
- Affiliation
- Ritsumeikan University
- Date
- March 26, 2014, noon
- Room
- room 2180
- Seminar
- Seminar Algebraic Topology
10/8-inequality is an inequality relating the signature and the second
Betti number of closed spin 4-manifolds.
This inequality was proved by M.Furuta by using a method of finite
dimensional approximation of Seiberg-Witten monopole equation as an
approach toward the 11/8-Conjecture.
The 11/8-Conjecture can be traced to the estimates of a homology
cobordism invariant "Bounding genus" for integral homology 3-spheres
introduced by Y.Matsumoto in his empirical study on the kernel of the
Rochlin invariants.
In this talk, I would like to explain briefly a proof of
10/8-inequality and give several applications. In particular, I would
like to introduce the bounding genus for rational homology spheres to
give their lower bounds in terms of Neumann-Siebenmann invariant.
