Seminarium z Topologii Algebraicznej
12:15-13:45, sala 2180
26.III.2014
Yoshihiro Fukumoto (Ritsumeikan University)
10/8-inequality and plumbed rational homology 3-spheres
Abstract:
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.
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