by

Bernd Ammann, Emmanuel Humbert

where the supremum runs over the set of all conformal classes on M, and where the infimum runs over all metrics in the given class.

We show that \tau(T^2,\chi)=2\sqrt{\pi} if \chi is ``the'' non-trivial spin structure on T^2. In order to calculate this invariant, we study the infimum as a function on the spin-conformal moduli space and we show that the infimum converges to 2\sqrt{\pi} at one end of the spin-conformal moduli space.

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The Paper was written on 20.12.2004

Last update 20.12.2004