An affirmative answer to a conjecture for Metoki class

In "The {G}el'fand-{K}alinin-{F}uks class and characteristic classes of transversely symplectic foliations" arXiv:0910.3414, Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in \ds\HGF{7}{2}{}{8} is decomposed as a product $\eta\wedge \omega$ of some leaf cohomology class $\eta$ and a transverse symplectic class $\omega$. We show that the same formula holds for Metoki class, which is a non-trivial element in \ds \HGF{9}{2}{}{14}. The result was conjectured by Kotschick and Morita, where they studied characteristic classes of symplectic foliations due to Kontsevich. Our proof depends on Groebner Basis theory using computer calculations.Comment: 11 plain text files which are output of Maple calculations and also raw materials. These are stored subdirectory anc as ancillary files. You can see the file size on appendice

Crosscap numbers of 2-bridge knots

We present a practical algorithm to determine the minimal genus of non-orientable spanning surfaces for 2-bridge knots, called the crosscap numbers. We will exhibit a table of crosscap numbers of 2-bridge knots up to 12crossings (all 362 of them).Comment: 17 pages, 7 figure