TOPOLOGICAL SYMMETRY GROUPS OF K4r+3

نویسندگان

  • Dwayne Chambers
  • Erica Flapan
  • John D. O’Brien
  • JOHN D. O’BRIEN
چکیده

We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of a complete graph of the form K4r+3 in S3. 1. Topological symmetry groups. Knowing the symmetries of a molecule helps to predict its chemical behavior. But, what exactly do we mean by “symmetries?” If we consider only rigid molecules, then the molecular symmetries are rotations, reflections, and reflections composed with rotations. Chemists have defined the point group of a molecule as its group of rigid symmetries. While this is a useful tool for rigid molecules, it can be misleading when applied to non-rigid molecules. For example, consider the molecule illustrated in Figure 1. The Cl on the far left is in front of the page, the Cl in the middle is behind the page, and the Cl on the right is in the page.

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تاریخ انتشار 2010