Dynamics on curve complexes and asymptotic structure of mapping class groups

利用曲线复形及其作用，研究了各种几何对象，如Kleinian群的变形空间，保持Heegaard分裂和桥分解的映射类群的特征标簇和子群，特别是它们的整体结构.我们还构造了Teichmuller空间的非Hausdorff紧化，并利用曲线复形上的映射类群作用，证明了它们的对称群与扩张的映射类群一致.

We studied various geometric objects, like deformation spaces of Kleinian groups, character varieties and subgroups of mapping class groups preserving Heegaard splittings and bridge decomposition, in particular their global structures, using curve complexes and their actions of mappingclass groups. We also constructed non-Hausdorff compactifications of Teichmuller spaces, and using the mapping class group actions on curve complexes, showed that their symmetry groups coincide with the extended mapping class groups.