Lower weight Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R^4

In this paper, we investigate the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R^4. In the case of formal Hamiltonian vector fields on R^2, we computed the relative Gel'fand-Kalinin-Fuks cohomology groups of weight <20 in the paper by Mikami-Nakae-Kodama. The main strategy there was decomposing the Gel'fand-Fucks cochain complex into irreducible factors and picking up the trivial representations and their concrete bases, and ours is essentially the same. By computer calculation, we determine the relative Gel'fand-Kalinin-Fuks cohomology groups of the formal Hamiltonian vector fields on R^4 of weights 2, 4 and 6. In the case of weight 2, the Betti number of the cohomology group is equal to 1 at degree 2 and is 0 at any other degree. In weight 4, the Betti number is 2 at degree 4 and is 0 at any other degree, and in weight 6, the Betti number is 0 at any degree.Comment: 133 page

A good presentation of (-2,3,2s+1)-type Pretzel knot group and R-covered foliation

Let K_s be a (-2,3,2s+1)-type Pretzel knot (s >= 3) and E(K_s)(p/q) be a closed manifold obtained by Dehn surgery along K_s with a slope p/q. We prove that if q>0, p/q >= 4s+7 and p is odd, then E(K_s)(p/q) cannot contain an R-covered foliation. This result is an extended theorem of a part of works of Jinha Jun for (-2,3,7)-Pretzel knot.Comment: 18 page

Taut foliations of torus knot complements

We show that for any torus knot $K(r,s)$, $|r|>s>0$, there is a family of taut foliations of the complement of $K(r,s)$, which realizes all boundary slopes in $(-\infty, 1)$ when $r>0$, or $(-1,\infty)$ when $r<0$. This theorem is proved by a construction of branched surfaces and laminations which are used in the Roberts paper~\cite{RR01a}. Applying this construction to a fibered knot ${K}'$, we also show that there exists a family of taut foliations of the complement of the cable knot $K$ of ${K}'$ which realizes all boundary slopes in $(-\infty,1)$ or $(-1,\infty)$. Further, we partially extend the theorem of Roberts to a link case

Role of interleukin-25 in development of spontaneous arthritis in interleukin-1 receptor antagonist-deficient mice

Interleukin (IL)-25, which is a member of the IL-17 family of cytokines, induces production of such Th2 cytokines as IL-4, IL-5, IL-9 and/or IL-13 by various types of cells, including Th2 cells, Th9 cells and group 2 innate lymphoid cells (ILC2). On the other hand, IL-25 can suppress Th1- and Th17-associated immune responses by enhancing Th2-type immune responses. Supporting this, IL-25 is known to suppress development of experimental autoimmune encephalitis, which is an IL-17-mediated autoimmune disease in mice. However, the role of IL-25 in development of IL-17-mediated arthritis is not fully understood. Therefore, we investigated this using IL-1 receptor antagonist-deficient (IL-1Ra-/-) mice, which spontaneously develop IL-17-dependent arthritis. However, development of spontaneous arthritis (incidence rate, disease severity, proliferation of synovial cells, infiltration of PMNs, and bone erosion in joints) and differentiation of Th17 cells in draining lymph nodes in IL-25-/- IL-1Ra-/- mice were similar to in control IL-25+/+ IL-1Ra-/- mice. These observations indicate that IL-25 does not exert any inhibitory and/or pathogenic effect on development of IL-17-mediated spontaneous arthritis in IL-1Ra-/- mice