Study on algebraic・topological・analytic K theory

我们得到了以下结果。1.我们确定了有限空间上与固定映射同伦的连续sap的一般结果.我们成功地推广了Gottlieb集和Varadarajan集的概念。我们研究了基本群的作用和局域化.得到了关于不定内积空间的一些结果。我们得到了将Tomita-Takesaki理论推广到 *-代数的结果。5.我们把在部分定义积下闭的族称为部分O*-代数，并研究了它的性质。我们用代数方法研究了一族无界算子.我们研究了一个27阶的射影平面。我们通过Oyama的方法确定了一个平移补群。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的Sherk平面的一个推广.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。研究了CCR-代数的性质。我们证明了Tomita-Takesaki定理的表示，这是研究的基础。给出了旗流形上黎曼域上真实的值多重次调和函数是全纯函数的真实的部分的条件.利用上同调群得到了真实的值多重次调和函数是全纯函数的真实的部分的一个条件。

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.