Self-avoiding walks on finitely ramified fractals

We present an exact real-space renormalization-group technique for self-avoiding walks performed on finitely ramified fractals. The exponent 1ν of the walks is found to be strongly affected by the geometry of the particular fractal. Also, the excluded volume is shown to be relevant for some fractals and irrelevant for others. For the Sierpinski gasket 1ν is shown to be equal to the fractal dimensionality of the gasket.