Topology of low dimensional manifolds with various geometric structures

Masaaki Ue研究了3-流形和4-流形，特别是带边界的4-流形。我们证明了3-流形的两个不变量，即Fukumoto-Furuta不变量和修正项，在球面3-流形的情况下是一致的。这些不变量来自这一研究领域的两个重要理论，Seiberg-Witten理论和Heegaard Floer同调理论。此外，我们表明，这些不变量是由以前已知的eta不变量。我们也给出了明确的限制的结构的4-流形有界的3-流形的这种类型的Fukumoto-Furuta不变量。

Masaaki Ue, the representative of this research has studied 3 and 4-manifolds, in particular 4-manifolds with boundary. We show that the two invariants for 3-manifolds, which are called Fukumoto-Furuta invariant and the correction term, coincide in case of spherical 3-manifolds. These invariants are derived from the two important theories for this area of research, Seiberg-Witten theory and Heegaard Floer homology theory. Moreover we show that these invariants are represented by the previously known eta invariants. We also give explicit constraints for the structures of 4-manifolds bounded by 3-manifolds of this type in terms of the Fukumoto-Furuta invariant.