Nafaa Chbili

THE JONES POLYNOMIALS OF FREELY PERIODIC KNOTS

For knots in S3 criteria for free periodicity are obtained in terms of the bracket and the Jones polynomials. The criteria introduced in this paper generalize the result obtained by Murasugi for the Jones polynomials of periodic knots.

Characterization of quasi-alternating Montesinos links

Let L be a quasi-alternating link at a crossing c. We construct an infinite family of quasi-alternating links from L by replacing the crossing c by a product of rational tangles, each of which extends c. Consequently, we determine an infinite family of quasi-alternating Montesinos links. This family includes all classes of quasi-alternating Montesinos links that have been detected by Widmer [Quasi-alternating Montesinos links, J. Knot Theory Ramifications18(10) (2009) 1459–1469]. We conjecture that this family contains all non-alternating quasi-alternating Montesinos links.

The skein polynomial of freely periodic knots

Abstract We use the first coefficient of the HOMFLY polynomial to find a necessary condition for a knot to be freely periodic. In particular for p =3 we obtain a simple but powerful criterion. As an application we show that some knot cannot have a certain free period.

The quantum SU(3) invariant of links and Murasugi's congruence

Abstract We use the SU (3) invariant introduced in [Enseign. Math. (2) 44 (1998) 325–360] to give a new criterion for periodic links. The result that we introduce in this paper may be seen as a generalization of Murasugis result about the Jones polynomial of periodic links [Pacific J. Math. 131 (1988) 319–329].

GRAPH SKEIN MODULES AND SYMMETRIES OF SPATIAL GRAPHS

In this paper, we compute the graph skein algebra of the punctured disk with two holes. Then, we apply the graph skein techniques developed here to establish necessary conditions for a spatial graph to have a symmetry of order

A new obstruction of quasialternating links

p

Quantum invariants and finite group actions on three-manifolds☆

, where

STRONG PERIODICITY OF LINKS AND THE COEFFICIENTS OF THE CONWAY POLYNOMIAL

p

THE MULTI-VARIABLE ALEXANDER POLYNOMIAL OF LENS BRAIDS

is a prime. The obstruction criteria introduced here extend some results obtained earlier for symmetric spatial graphs.

The Yamada polynomial of lens spatial graphs

We prove that the degree of the Q‐polynomial of any quasialternating link is less than its determinant. Therefore, we obtain a new and simple obstruction criterion for the link to be quasialternating. As an application, we identify some knots of 12 crossings or less and some links of 9 crossings or less that are not quasialternating. Our obstruction criterion applies also to show that there are only finitely many Kanenobu knots that are quasialternating. Moreover, we identify an infinite family of Montesinos links that are not quasialternating. 57M27