2 problems

Let $X$ be a smooth spin rational homology $S^1\times S^3$ which is oriented and homology oriented, and let $-X$ denote $X$ with reversed orientation but the same homology orientat…

Let $X$ be a smooth closed oriented $4$-manifold such that … where $\widetilde X$ is the universal abelian cover of $X$. The invariants $\lambda_{\,\rm{SW}}(X)$ and…