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math.GT2025
The bridge index and the braid index for twist positive knots
Keisuke Himeno
In general, the bridge index of a knot is less than or equal to its braid index. A natural question is when these two values coincide. Motivated by a conjecture of Krishna and Mort…
math.GT2025
Non-braid positive hyperbolic -space knots
Keisuke Himeno
An -space knot is a knot that admits a positive Dehn surgery yielding an -space. Many known hyperbolic -space knots are braid positive, meaning they can be represented as…
math.GT2025
The unoriented band unknotting numbers of torus knots
Keisuke Himeno
The unoriented band unknotting number of a knot is the minimum number of oriented or non-oriented band surgeries that turn the knot into the unknot. Batson introduced a certain non…