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Symmetries of spatial graphs and Simon invariants | | Ryo Nikkuni
; Kouki Taniyama
; | | Date: |
1 Aug 2007 | | Abstract: | An ordered and oriented 2-component link L in the 3-sphere is said to be
achiral if it is ambient isotopic to its mirror image ignoring the orientation
and ordering of the components. Kirk-Livingston showed that if L is achiral
then the linking number of L is not congruent to 2 modulo 4. In this paper we
study orientation-preserving or reversing symmetries of 2-component links,
spatial complete graphs on 5 vertices and spatial complete bipartite graphs on
3+3 vertices in detail, and completely determine the necessary conditions on
linking numbers and Simon invariants for such links and spatial graphs to be
symmetric. | | Source: | arXiv, 0708.0066 | | Services: | Forum | Review | PDF | Favorites | |
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