Incompressible surfaces in tunnel number one knot complements

A knot k in S3 has tunnel number one, if there exist an arc τ embedded in S3, with k∩τ=∂τ, such that S3−int N(k∪τ) is a genus 2 handlebody. s paper we construct for each integer g≥2, infinitely many tunnel number one knots, whose complement contain a closed incompressible surface of genus g.