Natural Properties of the Trunk of a Knot
نویسندگان
چکیده
The trunk of a knot in S3, defined by Makoto Ozawa, is a measure of geometric complexity similar to the bridge number or width of a knot. We prove that for any two knots K1 and K2, we have tr(K1#K2)= max{tr(K1), tr(K2)}, confirming a conjecture of Ozawa. Another conjecture of Ozawa asserts that any width-minimizing embedding of a knot K also minimizes the trunk of K. We produce several families of probable counterexamples to this conjecture.
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