We give examples of knots with some unusual properties of the crossing number of positive
diagrams or strand number of positive braid representations. In particular, we show that …

Using the band representation of the 3-strand braid group, it is shown that the genus of 3-
braid links can be read off their skein polynomial. Some applications are given, in particular …

We prove that a version of the Thurston–Bennequin inequality holds for Legendrian and
transverse links in a rational homology contact 3-sphere (M, ξ), whenever ξ is tight. More …

Using the Fiedler–Polyak–Viro Gauß diagram formulae we study the Vassiliev invariants of
degree 2 and 3 on almost positive knots. As a consequence we show that the number of …

It is proved in this note that the analogues of the Bennequin inequality which provide an
upper bound for the Bennequin invariant of a Legendrian knot in the standard contact three …

During the 2001 Georgia International Topology Conference, two problem sessions were
held concerning contact geometry. The rst was run by Emmanuel Giroux and focused on …

We prove a finiteness property of the values of the skein polynomial of homogeneous knots
that allows us to establish large classes of such knots to have arbitrarily unsharp Bennequin …

SOME INEQUALITIES BETWEEN KNOT INVARIANTS Page 1 May 22, 2002 14:35 WSPC/133-IJM
00129 International Journal of Mathematics, Vol. 13, No. 4 (2002) 373–393 c World Scientific …

We show that there are only finitely many homogeneous links whose Conway polynomial
has any given degree. Using this we give an example of an inhomogeneous, fibred knot …

Our main goal in this thesis is to describe the most important results on smooth and
Legendrian knots obtained from Heegaard Floer homology in the last ten years and …