Moduli space of JJ-holomorphic subvarieties

We study the moduli space of $J$-holomorphic subvarieties in a $4$-dimensional symplectic manifold. For an arbitrary tamed almost complex structure, we show that the moduli space of a sphere class is formed by a family of linear system structures as in algebraic geometry. Among the applications, we show various uniqueness results of $J$-holomorphic subvarieties, e.g. for the fiber and exceptional classes in irrational ruled surfaces. On the other hand, non-uniqueness and other exotic phenomena of subvarieties in complex rational surfaces are explored. In particular, connected subvarieties in an exceptional class with higher genus components are constructed. The moduli space of tori is also discussed, and leads to an extension of the elliptic curve theory.Comment: 45 pages. v2, presentation improved. v3, Corollary 3.9 adde

Poly(1-vinyl-1,2,4-triazolium) poly(ionic liquid)s: synthesis and the unique behavior in loading metal ions

Herein we report the synthesis of a series of poly(4-alkyl-1-vinyl-1,2,4-triazolium) poly(ionic liquid)s either via straightforward free radical polymerization of their corresponding ionic liquid monomers, or via anion metathesis of the polymer precursors bearing halide as counter anion. The ionic liquid monomers were first prepared via N-alkylation reaction of commercially available 1-vinyl-1,2,4-triazole with alkyl iodides, followed by anion metathesis with targeted fluorinated anions. The thermal properties and solubilities of these poly(ionic liquid)s have been systematically investigated. Interestingly, it was found that the poly(4-ethyl-1-vinyl-1,2,4-triazolium) poly(ionic liquid) exhibited an improved loading capacity of transition metal ions in comparison with its imidazolium counterpart.Comment: 18 pages, 9 figure