Nima Anvari
Published 2019-01-09Version 1
In a recent paper, Lin, Ruberman and Saveliev proved a splitting formula expressing the Seiberg-Witten invariant $\lambda_{SW}(X)$ of a smooth $4$-manifold with rational homology of $S^1\times S^3$ in terms of the Fr{\o}yshov invariant $h(X)$ and a Lefschetz number in reduced monopole Floer homology. In this note we observe that a similar splitting formula holds in reduced instanton Floer homology.
A splitting theorem for the Seiberg-Witten invariant of a homology $S^1 \times S^3$
The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant
3-cobordisms with their rational homology on the boundary
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