Abstract
We study the topology of SLE curves for κ>4. More precisely, we show that, a.s., there is no homeomorphism Φ:H‾→H‾, taking the range of one independent SLE curve to another for κ∈(4,8). Furthermore, we extend the result to κ≥8 by showing that there is no homeomorphism taking one SLE curve to another, when viewed as curves modulo parametrization.
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