To an integral homology 3-sphere Y, we assign a well-defined {\mathbb Z}-graded (monopole) homology MH*(Y, Ih(Q; h0)) whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow Ih(Q; h0), where Q is the unique U(1)-reducible monopole of the Seiberg-Witten equation on Y and h0 is a reference perturbation datum. The definition uses the moduli space of monopoles on Y \times {\mathbb R} introduced by Seiberg-Witten in studying smooth 4-manifolds. We show that the monopole homology MH*(Y, Ih(Q; h0)) is invariant among Riemannian metrics with same Ih(Q; h0). This provides a chamber-like structure for the monopole homology of integral homology 3-spheres. The assigned function MHSWF: \{Ih(Q; h0)\} \to \{MH*(Y, Ih(Q; h0))\} is a topological invariant (as Seiberg-Witten-Floer Theory).

To an integral homology 3-sphere Y, we assign a well-defined {\mathbb Z}-graded (monopole) homology MH*(Y, Ih(Q; h0)) whose construction in principle follows from the instanton Floer theory with the dependence of the spectral flow Ih(Q; h0), where Q is the unique U(1)-reducible monopole of the Seiberg-Witten equation on Y and h0 is a reference perturbation datum. The definition uses the moduli space of monopoles on Y \times {\mathbb R} introduced by Seiberg-Witten in studying smooth 4-manifolds. We show that the monopole homology MH*(Y, Ih(Q; h0)) is invariant among Riemannian metrics with same Ih(Q; h0). This provides a chamber-like structure for the monopole homology of integral homology 3-spheres. The assigned function MHSWF: \{Ih(Q; h0)\} \to \{MH*(Y, Ih(Q; h0))\} is a topological invariant (as Seiberg-Witten-Floer Theory).