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Published online by Cambridge University Press: 21 February 2011
We report a recent theoretical study of polymers moving on a random two-dimensional fluid surface. The metric of the liquid membrane is free to fluctuate and these new degrees of freedom couple to those of the polymers - as a result, the critical exponents describing the polymers are changed, but are nevertheless related to those in two dimensions. The relation to possible experimental studies on membranes with vanishing surface tension, which should search for new universal values of exponents u and 7, is discussed.