拓扑学100年(1935年以后)

100-Year of Topology

1935年以后的30多年中,拓扑学得到了大发展,主要表现在:一整套有效工具的建立,一系列重大结果的取得,在数学内外许多领域获得巨大的应用。拓扑学的技术及工具拓扑学的技术及工具,我们可以把它们纳入彼此有密切关联的四大范畴。同调及上同调 1935～1950年同调论成为一个成熟的系统理论。

After 1935,algebraic topology,armed with cohomology,homotopy,fiber bundles and K theory etc.has become a dominant discipline in mathematics,impacting almost all fields, especially algebraic number theory,algebraic geometry,differential geometry,functional analysis,even theoretical physics.From it emerged homological algebra,differential topology and global analysis.Recently,low-dimensional topology has made a lot of progress,and has become a center to unify whole mathematics.