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math.GT2025
Reducing spheres and weak reducing pairs for Heegaard surfaces in the -sphere
Sangbum Cho, Yuya Koda, Jung Hoon Lee
Given a Heegaard surface in the -sphere, we show that any non-separating weak reducing pair for the surface admits a reducing sphere that separates the two disks of the pair if…
math.GT2025
On symmetry and exterior problems of knotted handlebodies
Yuya Koda, Makoto Ozawa, Yi-Sheng Wang
The paper concerns two classical problems in knot theory pertaining to knot symmetry and knot exteriors. In the context of a knotted handlebody in a -sphere , the symme…
math.GT2025
Quantum enhancement polynomials associated with the canonical two-element tricbracket
Yuya Koda, Yuya Nishimura, Yuka Sakamoto
Quantum enhancement polynomials are invariants for oriented links, defined in association with an algebraic structure called a tribracket. In this paper, we focus on the particular…