Integral Klein bottle surgeries and Heegaard Floer homology

In this paper, we study which closed, connected, orientable three-manifolds X containing a Klein bottle arise as integral Dehn surgery along a knot in S³ . Such X are presentable as a gluing of the twisted I -bundle over the Klein bottle to a knot manifold, and we use a variety of Heegaard Floer-type invariants to generate surgery obstructions. Suppose that X is 8 -surgery along a genus two knot and arises by gluing the twisted I -bundle over the Klein bottle to an S³ knot complement. We show that X is an L -space, it must be the dihedral manifold (-1; 1/2, 1/2, 2/5) , and the surgery knot must be K=T(2,5) .