Floer homology of connected sum of homology 3-spheres
Let \(M\) be a homology 3-sphere. Then the space \(R(M)\) consisting of the conjugacy classes of SU(2) representations of the fundamental group \(\pi_1(M)\) can be identified with the set of critical points of the Chern-Simons functional on an infinite-dimensional space of gauge equivalence classes of connections on \(M\). The author studies the Floer homology group \(I_*(M)\) [\textit{A. Floer}, Commun. Math. Phys. 118, No. 2, 215-240 (1988; Zbl 0684.53027)] in the case when \(R(M)\) is of positive dimension. There is a generalization of Morse theory by Bott to the case when the critical point set is a nondegenerate smooth manifold. In the first part of the paper the author is concerned with an infinite-dimensional version of this case. In the second part the results are applied to the case when \(M\) is a connected sum of two homology spheres. The existence of a spectral sequence and some long exact sequence are established.
scientific article; zbMATH DE number 863696
scientific article