"Tangle sum and constructible spheres"


abstract
In this paper we discuss the bridge index of knots and tangles in relation with ``tangle sum'' operation. As a consequence, we solve the conjecture of R. Ehrenborg and M. Hachimori on the bridge index of knots contained in the 1-skeleton of constructible 3-spheres and 3-balls. We also improve a result of Armentrout.