2022-09-25T23:21:05Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000401152021-03-01T21:08:56ZSpin Structures on \\ Seiberg-Witten Moduli SpacesSasahira, Hirofumi138692415application/pdfLet $M$ be an oriented closed $4$-manifold with a spin$^c$ structure $\cL$. In this paper we prove that under a suitable condition for $(M,\cL)$ the Seiberg-Witten moduli space has a canonical spin structure and its spin bordism class is an invariant of $M$. We show that the invariant of $M=\#_{j=1}^l M_j$ is non-trivial for some spin$^c$ structure when $l$ is $2$ or $3$ and each $M_j$ is a $K3$ surface or a product of two oriented closed surfaces of odd genus. As a corollary, we obtain the adjunction inequality for the $4$-manifold. Moreover we calculate the Yamabe invariant of $M \# N_1$ for some negative definite $4$-manifold $N_1$. We also show that $M \# N_2$ does not admit an Einstein metric for some negative definite $4$-manifold $N_2$.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2006-12-27application/pdfJournal of mathematical sciences, the University of Tokyo313347363AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40115/files/jms130303.pdfeng