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Abstract: This is an expository paper. It is well known that a linear transformationcan be defined to have any desired action on a basis. From this fact, one canshow that every group homomorphism from Z^k to R^d extends to a homomorphismfrom R^k to R^d, and we will see other examples of discrete subgroups H ofconnected 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 veryclassical topic in geometry, the study of linkages.



Author: Dave Witte Morris

Source: https://arxiv.org/



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