text: We introduce a space of stable meromorphic differentials with poles of prescribed orders and define its tautological cohomology ring. This space, just as the space of holomorphic differentials, is stratified according to the set of multiplicities of zeros of the differential. The main goal of this paper is to compute the Poincar 'e-dual cohomology classes of all strata. We prove that all these classes are tautological and give an algorithm to compute them. In a second part of the paper we study the Picard group of the strata. We use the tools introduced in the first part to deduce several relations in these Picard groups.
  @cite_19: A suturing instrument for use in endoscopic surgery includes at one end of an elongated barrel a pair of jaws to grasp and release a needle. Within one of the jaws a recessed magnet properly positions, orients and holds the needle relative to the long axis of the barrel. In a preferred embodiment of an instrument with the magnet embedded in a lower jaw, the instrument includes a wire, which moves in parallel with an upper jaw as that jaw opens and closes, to push the needle out of the contact with the magnet in the lower jaw. The wire fits within a recess, and lies beneath the needle when the needle is in position and the jaws are closed. An alternative embodiment of the instrument includes in one of the jaws a magnet which is magnetized across the diameter. This magnet is oriented, relative to a long axis of the elongated barrel, such that the poles are perpendicular to the axis. A needle which has a magnet embedded in the suture end, or has the suture end which is coated with a material which is more magnetically permeable than the needle may be used with the instrument, to direct the needle to a particular position on the magnet.
summary: They gave an interpretation of the induction formula in genus 0 as a generalization of the completed cycle formula of Okounkov and Pandharipande (see @cite_19 ). For, now it is not clear if this generalized completed cycle formula has an extension to higher genera.