Titlebook: Rigidity and Symmetry; Robert Connelly,Asia Ivić Weiss,Walter Whiteley Book 2014 Springer Science+Business Media New York 2014 Cauchy iden

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Buildings and ,-Transitive Graphs,in 1947 that a finite trivalent graph can never be 6-transitive. We examine connections between the theory of .-transitive graphs and the classification of Moufang polygons, a class of graphs exhibiting “local” .-transitivity for large values of .. Moufang polygons are examples of buildings. Both of

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1069-5265 recent trends and advances in discrete geometry.Extends cla.This book contains recent contributions to the fields of rigidity and symmetry with two primary focuses: to present the mathematically rigorous treatment of rigidity of structures and to explore the interaction of geometry, algebra and com

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Mobility in Symmetry-Regular Bar-and-Joint Frameworks,nitesimal mechanism (respectively, state of self stress) within each irreducible representation of the point group of the framework. Similar conditions are found for symmetry-regular body-and-joint frameworks.

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Beauville Surfaces and Groups: A Survey,roups . (called Beauville groups) have this property? What can be said about the automorphism group and the fundamental group of .? Beauville surfaces are defined (as algebraic varieties) over the field . of algebraic numbers, so how does the absolute Galois group . act on them?

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One Brick at a Time: A Survey of Inductive Constructions in Rigidity Theory,tions were sufficient to generate all such frameworks. We also outline the use of inductive constructions in some recent areas of particularly active interest, namely symmetric and periodic frameworks, frameworks on surfaces, and body-bar frameworks. As the survey progresses we describe the key open problems related to inductions.

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Buildings and ,-Transitive Graphs, these notions were introduced by Jacques Tits in the study of algebraic groups. We give an overview of Tits’ classification results in the theory of spherical buildings (which include the classification of Moufang polygons as a special case) and describe, in particular, the classification of finite buildings.

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978-1-4939-4970-0Springer Science+Business Media New York 2014