On composite types of tunnel number two knots

摘要

Let K be a tunnel number two knot. Then, by considering the (g, b)-decompositions, K is one of (3, 0), (2, 1), (1, 2) or (0, 3)-knots. In this paper, we analyze the connected sum summands of composite tunnel number two knots and give a complete table of those summands from the point of view of (g, b)-decompositions.