Abstract

Coboundary operators for infinite frameworks

Highlights

  • Graph rigidity is an interdisciplinary field in which the central aim is to develop theoretical and computational techniques for identifying and characterising forms of rigidity and flexibility in discrete geometric structures

  • Mathematical Proceedings of the Royal Irish Academy and are typically categorised by the nature of these blocks and joints. Constraint systems of these forms are ubiquitous in engineering, in nature and in technology

  • Maddox [13] and others have extended some aspects of the classical theory to infinite matrices of operators, and we have found these techniques to be useful here

Read more

Summary

Introduction

Graph rigidity is an interdisciplinary field in which the central aim is to develop theoretical and computational techniques for identifying and characterising forms of rigidity and flexibility in discrete geometric structures. Mathematical Proceedings of the Royal Irish Academy and are typically categorised by the nature of these blocks and joints (e.g. bar-andjoint, body-and-bar and plate-and-hinge frameworks). Coboundary operators with a non-amenable graph structure can be bounded below, and in Section 5 we raise the interesting problem of whether there are natural classes of bar-joint frameworks for which the rigidity matrix gives rise to an operator that is bounded below on various spaces of velocity fields. We present an example of a bar-joint framework with a non-amenable graph structure for which the associated rigidity matrix determines a bounded operator that is neither compact nor bounded below

Coboundary operators
Norm approximation and compactness
The bounded below property
An application to rigidity theory

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.