The Unknotting Number Is Not Additive
14 hours ago
- #unknotting number
- #knot theory
- #mathematics
- Mark Brittenham and Susan Hermiller disproved a long-standing conjecture in knot theory about the additivity of unknotting numbers under connected sum.
- The conjecture stated that the unknotting number of a connected sum of two knots equals the sum of their individual unknotting numbers.
- They provided a counterexample using the connected sum of a (2,7) torus knot and its mirror image, showing its unknotting number is 5, not 6.
- Chao Wang and Yimu Zhang detailed a projection with 56 crossings where changing five specific crossings unknots the connected sum.
- The author verified the claim by redrawing the knot projection and demonstrating the sequence of steps to unknot it.