Does there exist a non trivial homomorphism from Thompson's group T to a linear group?

No: T is infinite, finitely presented and simple. Fg linear groups are residually finite, by Mal'cev's theorem. QED. 


Does there exist a non trivial homomorphism from Thompson's group T to a linear group? 


No: T is infinite, finitely presented and simple. Fg linear groups are residually finite, by Mal'cev's theorem. QED. 

