English

Abstract:
It has been conjectured that knots yielding a manifold with a finite \pi_1 via Dehn surgery are fibered and of tunnel number 1. In this talk, we survey recent studies of 'fibered double torus knots'. In particular, we actually construct fiber surfaces for some classes of such knots, and will see, in some cases (e.g. (1:1)-double torus knots etc), that fiberedness is algebraically determined. (Joint work with K. Murasugi)