Topology of manifolds and geometric structures

（1）无限维Lic群的拓扑（2）莫尔斯同伦代数与整体分析表示论与整体分析（5）动力系统（1）A.Kono利用自由loop群在基loop空间上的伴随作用确定了自由loop群的同伦环。A.Kono还研究了1-计数闭4维流形上主SU（2）丛的同构类与其分类空间的同伦类型之间的关系问题，并表明分类空间的同伦类型几乎决定了丛的同构类。（2）K.福谷考虑了无限维空间（例如模空间）上的Morsc函数族，并利用它们定义了上积和上同调算子。（3）K.Ucno和Y.Shimizu用代数几何方法研究了非线性微分方程的问题，得到了Kinizhink-Zamoldchikov方程的有趣结果。（4）M.Jimbo和T.Nomura利用表示论和量子群的方法得到了数学物理的某些结果。（5）H.lokubu研究了流形上动力系统的各种性质，得到了关于同宿轨道的结果。

(1)Topology of infinite dimensional Lic groups(2)Morse homotopyAlgebraic gcomctry and global analysisRepresentation thcory and global analysis(5)Dynamical systems(1)A.Kono detcrmined the homotopy ring of free loop groups using the adjoint action of the groups on the based loop spaces. A.Kono also studied the problem of the relations between the isomorphic classcs of principal SU(2) bundles over a 1-counccted closcd 4-dimensional manifolds and the homotopy type of their classifying spaces and showed that the homotopy type of the classifying spaces almost detcrmined the isomorphic classcs of the bundles.(2)K.Fukaya considered the family of Morsc functions on infinite dimensional spaces (e.g.moduli spaces)and defined sup products and cohomology operators using them.(3)K.Ucno and Y.Shimizu considered problems on nonlincar differential cquations using algebraic geometry and obtained intercsting results on Kinizhink-Zamoldchikov cquations.(4)M.Jimbo and T.Nomura obtained certain results on mathematical physics by using the methods of representation theory and quantum groups.(5)H.lokubu studied various propertics on dynamical systems on manifolds and got results on homoclinic orbits.