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I am thinking about homomorphisms $\mathrm{Hom}(\Gamma,G)$, where $G$ is a Lie group and $\Gamma$ is a discrete, finitely generated subgroup.

This questionThis question talked about the difference of infinitesimal rigidity vs. local rigidity and the second answerthe second answer shows that infinitesimal rigidity implies local rigidity. Are there examples (preferably in the context of discrete subgroups of Lie groups) such that $\mathrm{Hom}(\Gamma,G)$ is locally rigid, but not infinitesimally rigid?

I am thinking about homomorphisms $\mathrm{Hom}(\Gamma,G)$, where $G$ is a Lie group and $\Gamma$ is a discrete, finitely generated subgroup.

This question talked about the difference of infinitesimal rigidity vs. local rigidity and the second answer shows that infinitesimal rigidity implies local rigidity. Are there examples (preferably in the context of discrete subgroups of Lie groups) such that $\mathrm{Hom}(\Gamma,G)$ is locally rigid, but not infinitesimally rigid?

I am thinking about homomorphisms $\mathrm{Hom}(\Gamma,G)$, where $G$ is a Lie group and $\Gamma$ is a discrete, finitely generated subgroup.

This question talked about the difference of infinitesimal rigidity vs. local rigidity and the second answer shows that infinitesimal rigidity implies local rigidity. Are there examples (preferably in the context of discrete subgroups of Lie groups) such that $\mathrm{Hom}(\Gamma,G)$ is locally rigid, but not infinitesimally rigid?

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Earthliŋ
Earthliŋ
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I am thinking about homomorphisms $\mathrm{Hom}(\Gamma,G)$, where $G$ is a Lie group and $\Gamma$ is a discrete, finitely generated subgroup.

This question talked about the difference of infinitesimal rigidity vs. local rigidity and the second answer shows that infinitesimal rigidity implies local rigidity. Are the two notions equivalent, or are there examples (preferably in the context of discrete subgroups of Lie groups) such that $\mathrm{Hom}(\Gamma,G)$ is locally rigid, but not infinitesimally rigid?

I am thinking about homomorphisms $\mathrm{Hom}(\Gamma,G)$, where $G$ is a Lie group and $\Gamma$ is a discrete, finitely generated subgroup.

This question talked about the difference of infinitesimal rigidity vs. local rigidity and the second answer shows that infinitesimal rigidity implies local rigidity. Are the two notions equivalent, or are there examples (preferably in the context of discrete subgroups of Lie groups) such that $\mathrm{Hom}(\Gamma,G)$ is locally rigid, but not infinitesimally rigid?

I am thinking about homomorphisms $\mathrm{Hom}(\Gamma,G)$, where $G$ is a Lie group and $\Gamma$ is a discrete, finitely generated subgroup.

This question talked about the difference of infinitesimal rigidity vs. local rigidity and the second answer shows that infinitesimal rigidity implies local rigidity. Are there examples (preferably in the context of discrete subgroups of Lie groups) such that $\mathrm{Hom}(\Gamma,G)$ is locally rigid, but not infinitesimally rigid?

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Earthliŋ
Earthliŋ
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Infinitesimal rigidity vs. local rigidity

I am thinking about homomorphisms $\mathrm{Hom}(\Gamma,G)$, where $G$ is a Lie group and $\Gamma$ is a discrete, finitely generated subgroup.

This question talked about the difference of infinitesimal rigidity vs. local rigidity and the second answer shows that infinitesimal rigidity implies local rigidity. Are the two notions equivalent, or are there examples (preferably in the context of discrete subgroups of Lie groups) such that $\mathrm{Hom}(\Gamma,G)$ is locally rigid, but not infinitesimally rigid?