The Bennequin number of n-trivial closed n-braids is negative
  A famous result of Bennequin states that for any braid representative of the unknot the Bennequin number is negative. We will extend this result to all n-trivial closed n-braids. This is a class of infinitely many knots closed under taking mirror images. Our proof relies on a non-standard parametrization of the Homfly polynomial. 
Oliver T. Dasbach and Xiao-Song Lin