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Arthur Moritz Schoenflies (German: [ˈʃøːnfliːs]; 17 April 1853 – 27 May 1928), sometimes written as Schönflies, was a German mathematician, known for his contributions to the application of group theory to crystallography, and for work in topology.
The Schoenflies (or Schönflies) notation, named after the German mathematician Arthur Moritz Schoenflies, is a notation primarily used to specify point groups in three dimensions. Because a point group alone is completely adequate to describe the symmetry of a molecule , the notation is often sufficient and commonly used for spectroscopy .
Schoenflies (or Schönflies) displacement (or motion) named after Arthur Moritz Schoenflies is a rigid body motion consisting of linear motion in three dimensional space plus one orientation around an axis with fixed direction. [1]
This diffeomorphism then provides the smooth solution to the Schoenflies problem. The Jordan-Schoenflies theorem can be deduced using differential topology. In fact it is an immediate consequence of the classification up to diffeomorphism of smooth oriented 2-manifolds with boundary, as described in Hirsch (1994). Indeed, the smooth curve ...
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The superscript doesn't give any additional information about symmetry elements of the space group, but is instead related to the order in which Schoenflies derived the space groups. This is sometimes supplemented with a symbol of the form Γ x y {\displaystyle \Gamma _{x}^{y}} which specifies the Bravais lattice.
Earlier, Jordan's proof and another early proof by Charles Jean de la Vallée Poussin had already been critically analyzed and completed by Schoenflies (1924). [ 15 ] Due to the importance of the Jordan curve theorem in low-dimensional topology and complex analysis , it received much attention from prominent mathematicians of the first half of ...