Liftings of surfaces in the plane

2025/05/24 by Karpenkov, Oleg, Servatius, Brigitte, Servatius, Herman
#05C10 #52C25 #57Q99 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.18841

Abstract

In this note we provide a topological definition of Maxwell-Cremona liftings for non-planar frameworks of surfaces (both oriented and non-oriented). In the non-oriented case we give an estimate on the dimension of self-stresses, when the frameworks will posses a non-trivial lifting.

Citations

• A differential approach to Maxwell-Cremona liftings
• A Cosheaf Theory of Reciprocal Figures: Planar and Higher Genus Graphic Statics
• A Toroidal Maxwell-Cremona-Delaunay Correspondence
• Liftings and stresses for planar periodic frameworks

Related

• A differential approach to Maxwell-Cremona liftings
• Stressability of Semi-Discrete Frameworks
• Liftings and stresses for planar periodic frameworks
• On traces of d-stresses in the skeletons of lower dimensions of homology d-manifolds
• Statics and kinematics of frameworks in Euclidean and non-Euclidean geometry