Title: On Dehn surgeries between S1xS2 and lens spaces

Abstract: We consider knots in S1 x S2 with a Dehn surgery to a lens space and how this parallels what happens for knots in S3. The Cyclic Surgery Theorem enables a classification for non-longitudinal surgeries, while Berge's families of doubly primitive knots in S3 motivate our 

conjectural classification for longitudinal surgeries. We will compare this conjectural picture with the Berge Conjecture pointing out their differences and similarities.