• Honam Mathematical Journal
• /
• v.37 no.2
• /
• pp.235-244
• /
• 2015

It is known that there is an infinite family of general pretzel knots, each of which has Rasmussen s-invariant equal to the negative value of its signature invariant. For an instance, homologically ${\sigma}$-thin knots have this property. In contrast, we find an infinite family of 4-strand pretzel knots whose Rasmussen invariants are not equal to the negative values of signature invariants.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.4
• /
• pp.1139-1148
• /
• 2015

For any alternating knot, it is known that the double branched cover of the 3-sphere branched over the knot is an L-space. We show that the three-fold cyclic branched cover is also an L-space for any genus one alternating knot.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.1019-1029
• /
• 2009

We show that every bridge surface of certain types of (1, 1) prime knot has the disjoint curve property. Also we determine when a bridge surface of a pretzel knot of type (.2, 3, n) has the disjoint curve property.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.421-431
• /
• 2024

In this paper, we characterize amphicheiral 2-bridge knots with symmetric union presentations and show that there exist infinitely many amphicheiral 2-bridge knots with symmetric union presentations with two twist regions. We also show that there are no amphicheiral 3-stranded pretzel knots with symmetric union presentations.