Künneth formula for \(SO(3)\) Floer homology (Q1296319)

In order to characterize the \(SO(3)\) Floer homology, one has to take the torsion elements into consideration. Therefore it is important to understand the Künneth formula for integral coefficients. In this paper, the author gives an analytic proof of the Künneth formula for integral coefficients and \(SO(3)\) flat connections. His approach is quite different from that of \textit{P. J. Braam} and \textit{S. K. Donaldson} [Floer's work on instanton homology, knots and surgery, in `The Floer memorial volume', Prog. Math. 133, 195-256 (1995; Zbl 0996.57516); Fukaya-Floer homology and gluing formulae for polynomial invariants, ibid., 257-281 (1995; Zbl 0996.57517)] and more direct to understanding the chain complex and the boundary map. The author also gives a universal coefficient theorem for the \(SO(3)\) Floer homology, which is quite easy from the algebraic point of view. The method of this paper may be useful to some general cases, like the Heegaard splitting for an integral homology three-sphere.