5 papers
Non-triviality of generalized alternating knots
Makoto Ozawa
In this article, we consider alternating knots on a closed surface in the 3-sphere, and show that these are not parallel to any closed surface disjoint from the prescribed one.
Morse position of knots and closed incompressible surfaces
Makoto Ozawa
In this paper, we study on knots and closed incompressible surfaces in the 3-sphere via Morse functions. We show that both of knots and closed incompressible surfaces can be isotop…
Closed incompressible surfaces in the complements of positive knots
Makoto Ozawa
We show that any closed incompressible surface in the complement of a positive knot is algebraically non-split from the knot, positive knots cannot bound non-free incompressible Se…
Impossibility of obtaining split links from split links via twistings
Makoto Ozawa
We show that if a split link is obtained from a split link in by -Dehn surgery along a trivial knot , then the link is splittable. That is to say, it is…
Additivity of free genus of knots
Makoto Ozawa
We show that free genus of knots is additive under connected sum.