Liftings of surfaces in the plane
Oleg Karpenkov, Brigitte Servatius, Herman Servatius
TL;DR
This paper introduces a topological approach to Maxwell-Cremona liftings for frameworks on surfaces, providing estimates on self-stress dimensions that determine when non-trivial liftings occur.
Contribution
It offers a new topological definition for liftings of surface frameworks and estimates self-stress dimensions in non-oriented cases, extending classical concepts.
Findings
Topological definition of Maxwell-Cremona liftings for surface frameworks
Estimate of self-stress dimensions in non-oriented frameworks
Conditions for the existence of non-trivial liftings
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.
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