Spin 4-manifolds with signature \(=-32\) (Q5946657)

The authors prove that if \(X\) is a closed spin 4-dimensional manifold with signature \(\text{sign}(X)=-32\), then \(b_2^+(X)\geq 6\). They give three different proofs of their theorem. The first proof is a consequence of a generalized adjunction inequality proven by the two first named authors and \textit{N. Minami} [J. Math. Sci., Tokyo 8, No. 1, 157-176 (2001; Zbl 0976.57030)]. The other proofs use stable-homotopy formulations of the Seiberg-Witten invariants.