Study on algebraic・topological・analytic K theory

我们得到了以下结果：1.我们确定了与有限素描上的固定映射同位的连续SAP上的一般结果。我们成功地推广了Gottlieb集和Varadarajan集的概念。我们研究了基本群和定域化的作用。得到了具有不定内积的空间的一些结果。得到了将Tomita-Takesaki理论推广到*-代数的一个结果。我们称部分定义乘积下的闭族为偏O*-代数，并研究了该代数的性质。研究了一类无界算子的代数性质。我们研究了一个27阶射影平面。我们用Oyama的方法确定了翻译补体基团。我们还构造了一些新的27阶平移平面。此外，我们还得到了一般阶Sherk平面的推广。研究了一维环面上齐次Banach代数的局部代数。我们在一定程度上确定了C型的结构。我们研究了CCR-代数的性质。我们证明了一个表示的Tomita-Takesaki定理，这是研究的基础。我们确定了实值多重次调和函数是旗形上黎曼域上全纯函数的实部的一个条件。利用上同调群得到了实值多重次调和函数是全纯函数实部的一个条件。

We obtained the following results.1. We determined general results on continuous saps which are honotopic to a fixed map on the finite sketetons.2. We succeeded to generalize the concepts of Gottlieb sets and Varadarajan sets. We studied the actions of the fundamental groups and localizations.3. We obtained some results on the spaces with an indefinite inner-product.4. We obtained a result on a generatization of Tomita-Takesaki theory to a *-algebra.5. We call a family which is closed under a partially defined product a partial O*-algebra, and studied the properties of the algebra. We studied a family of unbounded operators algebraically.6. We studied a projective plane of order 27. We determined a translation complement group by a method of Oyama.7. We also constructed some new translation planes of order 27. Furthermore we obtained a generatization of the Sherk plane of general order.8. We studied the local algebra of homogeneous Banach algebra on 1-dimensioned torus. We determined the structure of type-C to some extent.9. We studied the properties of CCR-algebras. We proved Tomita-Takesaki theorem for a representation which is fundamental for the study.10. We determined a condition for real valued plurisubharmonic function to be the real part of a holomorphic function on a Riemann domain over a flag manifold.11. We obtained a condition for real valued plurisubharmonic function to be the real part of a holomorphic function, using cohomology group.