By computing K-homolngy and K-theory, information about topology and geometry of geometric spaces can be obtained.With the help of homotopy, the range of calculable spaces is extended.

• 摘要通过计算K同调群和K群，可以得到几何空间的拓扑几何信息，借助于同伦可以拓展可计算空间的范畴。