Advances and Applications in Discrete Mathematics
Volume 17, Issue 2, Pages 211 - 242
(April 2016) http://dx.doi.org/10.17654/AADMApr2016_211_242 |
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THE CONFIGURATION SPACE OF SPATIAL POLYGONS WITH RESTRICTION ON THE INTERIOR ANGLES
Yasuhiko Kamiyama
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Abstract: Given a string of npositive real numbers, let be the configuration space of planar polygons having side lengths Many topological properties of are already known: For example, the condition under which is nonempty is known. Also, the condition for which is connected is known. Moreover, when is a closed surface and a formula to compute is also known.
Recently, motivated by chemistry, the configuration space of certain spatial polygons was constructed: The space consists of spatial polygons having side lengths such that the interior angles are all equal to except for two angles at the successive vertices. We denote the configuration space by In this paper, we study which properties for also hold for for the case that there are at most two different |
Keywords and phrases: polygon space, interior angle, Bott-Morse function. |
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