Reading Group in Rigidity Theory

From MathWiki

This informal group will meet regularly on Wednesday mornings 10-11:30 in Ross N627. Contact Walter Whiteley whiteley@mathstat.yorku.ca At our first session (January 17) we reviewed some of the core definitions (Rigidity, First-order or Static rigidity, and Global Rigidity). Here is a DRAFT map of the key concepts, which I will try to keep updated as we progress: Rigidity Concepts


There are a nice set of papers (some dated) over a range of rigidity theory as well as protein flexibility, available for download at http://biophysics.asu.edu/banf/list.php flexweb.asu.edu [1] is a web site with a lot of material (and an online algorithm) for the study of the rigidity and flexibility of biomolecules.

All issues of Structural Topology (which published a number of the early articles in this generation of work on rigidity) are accessible at the Barcelona web site: http://www-iri.upc.es/people/ros/StructuralTopology/

Some other articles, including recent articles and draft introductory chapters for the never completed book on Rigidity (23 on his list) are downloadable at: http://www.math.cornell.edu/~connelly/ Algorithms actually used focus on the 'pebble game' in different variations. See the flexweb implementation for 2|V|-3 at http://flexweb.asu.edu/software/pebble_game/2D_interactive/ See also the interactive Java program for general counts at http://www.cs.umass.edu/~alee/bodyBar/

People interested in Adnan Sljoka's recent thesis: "Counting for Rigidity, Flexibility and Extensions via the Pebble Game Algorithm" can download it from http://www.math.yorku.ca/~adnanslj/thesis.pdf

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Inductive Techniques There are a number of papers developing rigidity results with inductive techniques. For Plane Rigidity, this associated with Henneberg Methods. Here is the link to a preprint which surveys a number of methods for the plane, including a duality between methods, for the special case of planar graphs: Bases and Circuits for 2-Rigidity