What is a superrigid subgroup?

2007/12/14 by Dave Witte Morris, Morris, Dave Witte
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #History and Overview (math.HO) #Metric Geometry (math.MG) #math.HO #math.MG

paper · pdf · doi:10.48550/arxiv.0712.2299

18 pages, 7 figures

arxiv created 2007/12/14 · openalex publication_date 2007/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is an expository paper. It is well known that a linear transformation can be defined to have any desired action on a basis. From this fact, one can show that every group homomorphism from Z^k to R^d extends to a homomorphism from R^k to R^d, and we will see other examples of discrete subgroups H of connected groups G, such that the homomorphisms defined on H can ("almost") be extended to homomorphisms defined on all of G. This is related to a very classical topic in geometry, the study of linkages.

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