4 citations · 5 across the 4 of their papers we have counts for
4 papers · 1 filter
On a generalized Jones conjecture
Keiko Kawamuro
We solve the Jones conjecture, which states that the exponent sum in a minimal braid representation of a knot in S^3 is a knot invariant, by proving a generalized version of the or…
On Transverse Knots and Branched Covers
Shelly Harvey, Keiko Kawamuro, Olga Plamenevskaya
We study contact manifolds that arise as cyclic branched covers of transverse knots in the standard contact 3-sphere. We discuss properties of these contact manifolds and describe…
Khovanov-Rozansky homology and the braid index of a knot
Keiko Kawamuro
We prove the existence of a knot whose braid index the Morton-Franks-Williams inequality fails to detect but a related inequality (KR-MFW inequality), which uses new information of…
Non-sharpness of the Morton-Franks-Williams inequality
Keiko Kawamuro
We give conditions on a knot on which the Morton-Franks-Williams inequality is not sharp. As applications, we show infinitely many examples of knots where the inequality is not sha…