Low-dimensional topology. In mathematics , low-dimensional topology is the branch of topology that studies manifolds of four or fewer dimensions .
Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory , and braid groups . It can be regarded as a part of geometric topology . A number of advances starting in the 1960s had the effect of emphasising low dimensions in topology. The solution by Smale , in 1961, of the Poincaré conjecture in higher dimensions made dimensions three and four seem the hardest; and indeed they required new methods, while the freedom of higher dimensions meant that questions could 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. Richard Feynman. Henri Poincaré. French mathematician, physicist, engineer, and philosopher of science Jules Henri Poincaré (,[4] ;[5][6][7] French: [ɑ̃ʁi pwɛ̃kaʁe] ( listen);[8][9] 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.
He is often described as a polymath, and in mathematics as "The Last Universalist",[10] since he excelled in all fields of the discipline as it existed during his lifetime. John von Neumann.