Exceptional surgeries on alternating knots

We give a complete classification of exceptional surgeries on hyperbolic alternating knots in the 3-sphere. As an appendix, we also show that the Montesinos knots M (-1/2, 2/5, 1/(2q + 1)) with q at least 5 have no non-trivial exceptional surgeries. This gives the final step in a complete classification of exceptional surgery on arborescent knots.Comment: 30 pages, 19 figures. v2: recomputation performed via the newest version of hikmot, v3: revised according to referees' comments, to appear in Comm. Anal. Geo

Cosmetic banding on knots and links

We present various examples of cosmetic bandings on knots and links, that is, bandings on knots and links leaving their types unchanged. As a byproduct, we give a hyperbolic knot which admits exotic chirally cosmetic surgeries yielding hyperbolic manifolds. This gives a counterexample to a conjecture raised by Bleiler, Hodgson and Weeks.Comment: 17 pages, 15 figures, with an appendix by Hidetoshi Masa