The Rasmussen invariants and the sharper slice-Bennequin inequality on knots

An estimate of the Rasmussen invariant for links and the determination for certain links

“…The positive knot and the knot cobordism constructed in the above proof are different from those constructed in [7] to prove the inequality (6). Remark 4.9.…”

“…In the proof of the above theorem, we use an argument similar to that in [7], where the following lemma was shown. …”

“…where ν = 2τ or s. In this article, we improve these inequalities as follows, combining the argument in the proof of Theorem 1.1 with that in the proof of the inequality (6) in [7]. Theorem 1.3.…”

“…In [7] the author showed that the following stronger inequality holds for any knot K and its diagram D K with O ≥ (D K ) ≥ 1:…”

The Rasmussen invariant of a homogeneous knot

“…Our motivation for studying the Rasmussen invariant is to describe s(K) in terms of a given diagram of a knot K to better understand g * (K). From this point of view, some estimations of the Rasmussen invariant are known (Plamenevskaya [24], Shumakovitch [30] and Kawamura [12]. See also Stoimenow [32]).…”