Formal $3$-deformations of $2$-polyhedra
نویسندگان
چکیده
منابع مشابه
Small deformations of polygons and polyhedra
We describe the first-order variations of the angles of Euclidean, spherical or hyperbolic polygons under infinitesimal deformations such that the lengths of the edges do not change. Using this description, we introduce a quadratic invariant on the space of first-order deformations of a polygon. For convex polygons, this quadratic invariant has a positivity property, leading to a new proof of t...
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We show that certain twisting deformations of a family of supersolvable groups are simple as Hopf algebras. These groups are direct products of two generalized dihedral groups. Examples of this construction arise in dimensions 60 and pq, for prime numbers p, q with q|p − 1. We also show that certain twisting deformation of the symmetric group is simple as a Hopf algebra. On the other hand, we p...
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Let X be a complex algebraic variety, and X◦ ⊂ X be the smooth part of X. Consider the scheme L(X) of formal arcs in X. The C-points of L(X) are just maps D = SpecC[[t]] → X (see, for example, [DL] for a definition of L(X) as a scheme). Let L◦(X) be the open subscheme of arcs whose image is not contained in X \X◦. Fix an arc γ : D → X in L◦(X), and let L(X)γ be the formal neighborhood of γ in L...
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We generalize Cauchy’s celebrated theorem on the global rigidity of convex polyhedra in Euclidean 3-space E to the context of circle polyhedra in the 2-sphere S. We prove that any two convex and proper non-unitary c-polyhedra with Möbiuscongruent faces that are consistently oriented are Möbius-congruent. Our result implies the global rigidity of convex inversive distance circle packings in the ...
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The L∞-algebra controlling simultaneous deformations of a morphism of associative algebras and its domain and codomain is described. Isomorphism of the cohomology of this L∞-algebra with the classical construction is shown.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-1973-0331397-2