2 citations · 2 across the 3 of their papers we have counts for
4 papers
Unknotting number for Lorenz knots
Lilya Lyubich
The unknotting number of a positive braid with n strands and k intersections is known to be equal to (k-n+1)/2. We consider Lorenz knots (which are positive braids) and, using a di…
On cycles and coverings associated to a knot
Lilya Lyubich, Mikhail Lyubich
We consider the space of all representations of the commutator subgroup of a knot group into a finite abelian group Σ, together with a shift map σ_x. This is a finite dynamical sys…
On zeros of the Alexander polynomial of an alternating knot
Lilya Lyubich, Kunio Murasugi
We prove that for any zero α of the Alexander polynomial of a two-bridge knot, -3 < Re(α) < 6. Furthermore, for a large class of two-bridge knots we prove -1<Re(α).
Periodic orbits of a dynamical system related to a knot
Lilya Lyubich
We consider the space of all representations of the commutator subgroup of a knot group into Z/p, p is prime. As proven by D. Silver and S. Williams, this space can be completely d…