Measurement of the topological branching fractions of the $\tau$ lepton at LEP

Using data collected with the L3 detector at LEP from 1992 to 1995 on the Z peak, we determine the branching fractions of the $\tau$ lepton into one, three and five charged particles to be: \begin{eqnarray*} & {\cal{B}}(\tau\rightarrow (1-prong)) & = 85.274 \pm 0.105 \pm 0.073 \% , \\ & {\cal{B}}(\tau\rightarrow (3-prong)) & = 14.556 \pm 0.105 \pm 0.076 \%, \\ & {\cal{B}}(\tau\rightarrow (5-prong)) & = \phantom{0} 0.170 \pm 0.022 \pm 0.026 \%. \end{eqnarray*} \noindent The first uncertainties are statistical and the second systematic. The accuracy of these measurements alone is similar to that of the current world avera