We give a new construction of monopole Floer homology for spin-c rational
homology 3-spheres. As applications we define two invariants of certain smooth
compact 4-manifolds with b_1=1 and b^+=0.Comment: 60 pages, to appear in Duke J. Math. v2: Minor improvements
concerning orientations on pages 18-21. v3: Two new sections 4 and 14 have
been added
