2 8 A ug 2 00 7 Lehmer ’ s Question , Knots and Surface Dynamics

ar X iv : 0 70 8 . 05 14 v 1 [ m at h . G T ] 3 A ug 2 00 7 Invariants of genus 2 mutants

Pairs of genus 2 mutant knots can have different Homfly polynomials, for example some 3-string satellites of Conway mutant pairs. We give examples which have different Kauffman 2-variable polynomials, answering a question raised by Dunfield et al in their study of genus 2 mutants. While pairs of genus 2 mutant knots have the same Jones polynomial, given from the Homfly polynomial by setting v =...

m at h . G T ] 1 5 A ug 2 00 7 HIGH DISTANCE KNOTS

We construct knots in S with Heegaard splittings of arbitrarily high distance, in any genus. As an application, for any positive integers t and b we find a tunnel number t knot in the three-sphere which has no (t, b)–decomposition.

ar X iv : 0 90 8 . 01 53 v 1 [ m at h . G T ] 2 A ug 2 00 9 On Fibonacci knots

We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when n 6≡ 0 (mod 4) and (n, j) 6= (3, 3), the Fibonacci knot F (n) j is not a Lissajous knot. keywords: Fibonacci polynomials, Fibonacci knots, continued fractions

ar X iv : 0 80 8 . 36 90 v 1 [ qu an t - ph ] 2 7 A ug 2 00 8 Entanglement dynamics of two - qubit system in different types of noisy channels ∗

X iv :0 80 8. 36 90 v1 [ qu an tph ] 2 7 A ug 2 00 8 Entanglement dynamics of two-qubit system in different types of noisy channels ∗ C. J. Shan, J. B. Liu, W. W. Cheng, T. K. Liu, Y. X. Huang, and H. Li College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China (Dated: August 27, 2008) Abstract In this paper, we study entanglement dynamics of a two-qubit extende...

ar X iv : 0 70 8 . 26 18 v 1 [ as tr o - ph ] 2 0 A ug 2 00 7 Using Local Volume data to constrain Dark Matter dynamics