Klein bottle surgery and genera of knots

In this paper, we study the creation of Klein bottles by surgery on knots in the 3-sphere. For non-cabled knots, it is known that the slope corresponding to such surgery is an integer. We give an upper bound for the slopes yielding Klein bottles in terms of the genera of knots. 1. Introduction. In this paper, we will study the creation of Klein bottles by surgery on knots in the 3-sphere S3. Let K be a knot in S3, and let E(K) be its exterior. A slope on ∂E(K) is the isotopy class of an essential simple closed curve in ∂E(K). As usual, the slopes on ∂E(K) are parameterized by Q ∪ {1/0}