Physics Impact of a Precise Determination of the Top Quark Mass at an $e^{+}e^{-}$ Linear Collider

At a prospective e+e- Linear Collider (LC) a very precise determination of the top quark mass with an accuracy of $delta m_t <= 100 MeV$ will be possible. This is to be compared with the envisaged accuracy of $delta m_t = 1-2 GeV$ at the Tevatron and the LHC. We discuss the physics impact of such a precise determination of m_t, focusing on the Standard Model (SM) and its minimal supersymmetric extension (MSSM). In particular, we show the importance of a precise knowledge of m_t for electroweak precision observables, and for Higgs physics and the scalar top sector of the MSSM. Taking the mSUGRA model as a specific example, we furthermore demonstrate the importance of a precise m_t value for the prediction of sparticle masses and for constraints on the parameter space allowed by the relic density. The uncertainty in m_t also significantly affects the reconstruction of the supersymmetric high scale theory. We find that going from hadron collider to LC accuracy in m_t leads to an improvement of the investigated quantities by up to an order of magnitude.