Record link: 
http://hdl.handle.net/20.500.12708/136152
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Title: 
Equilibrium stressability of multidimensional frameworks
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Citation: 
Karpenkov, O., Müller, C., Panina, G., Servatius, B., Servatius, H., & Siersma, D. (2022). Equilibrium stressability of multidimensional frameworks. European Journal of Mathematics, 8(1), 33–61. https://doi.org/10.1007/s40879-021-00523-3
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Publisher DOI: 
10.1007/s40879-021-00523-3
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Publication Type: 
Article - Original Research Article
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Language: 
English
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Authors: 
Karpenkov, Oleg 
Müller, Christian 
Panina, Gaiane 
Servatius, Brigitte 
Servatius, Herman 
Siersma, Dirk 
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Organisational Unit: 
E104-04 - Forschungsbereich Angewandte Geometrie 
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Journal: 
European Journal of Mathematics 
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ISSN: 
2199-675X
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Date (published): 
Mar-2022
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Number of Pages: 
29
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Publisher: 
Springer Nature
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Peer reviewed: 
Yes
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Keywords: 
Cayley algebra; Discrete multiplicative 1-form; Equilibrium stress; Framework; Lifting; Maxwell–Cremona correspondence; Self-stress; Tensegrity
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Abstract: 
We prove an equilibrium stressability criterion for trivalent multidimensional frameworks. The criterion appears in different languages: (1) in terms of stress monodromies, (2) in terms of surgeries, (3) in terms of exact discrete 1-forms, and (4) in Cayley algebra terms.
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Project title: 
Diskrete Flächen mit vorgeschriebener mittlerer Krümmung: P 29981-N35 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF)) 
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Research Areas: 
Fundamental Mathematics Research: 100%
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Science Branch: 
1010 - Mathematik: 100%
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