In the rapid development of topology after 1945, a distinction was drawn between a fields of algebraic topology typified by homotopy theory, geometric topology sustaining a Poincaré conjecture as its biggest unresolved condition, & differential topology as the learn mostly of differential structures, with Morse theory as its natural technique. These fields everthing rested in general topology, which was the learn of the general topological space. This classification would came to seem further unreal, by owning a passing of years.

a total of advances starting in the Sixties experienced the result of changing geometrical topology. A guide by Smale, around 1961, of a Poincaré conjecture inside higher dimensions mass produced dimensions 3 & 4 seem a hardest; & indeed it mandatory freshly methods, when the freedom of higher dimensions intended that questions can be reduced to computational methods available in surgery theory. Thurston's geometrization conjecture, formulated in the late 1970s, offered a framework that suggested geometry and topology were closely intertwined in low dimensions, and Thurston's proof of geometrization for Haken manifolds utilized a variety of tools from previously only weakly linked areas of mathematics. Vaughan Jones' discovery of the Jones polynomial within the early 1980s non lone led knot theory in recently directions however bring about to however mysterious modems between online-dimensional topology & mathematical natural philosophy.

Overall, this progress has led to better integration of a field into the rest of math.

View likewise: list of geometric topology topics

de:Geometrische Topologie