The mapping class group and the Meyer function for plane curves

For each d>=2, the mapping class group for plane curves of degree d will be defined and it is proved that there exists uniquely the Meyer function on this group. In the case of d=4, using our Meyer function, we can define the local signature for 4-dimensional fiber spaces whose general fibers are non-hyperelliptic compact Riemann surfaces of genus 3. Some computations of our local signature will be given.Comment: 24 pages, typo adde

Classification of R-operators

We classified the R-operators which satisfy the quantum Yang–Baxter equation on a function space. In this study, we gave all the meromorphic solutions of the system of the functional equations which is a necessary and sufficient condition for the R-operator to satisfy the Yang–Baxter equation. Most of the solutions were expressed in terms of the elliptic, trigonometric and rational functions