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*Hideki Omori *

Introduction to noncommutative differential geometry

*(Lobachevskii Journal of Mathematics,
Vol.4, pp.13-46)*

It is getting a major understanding that the {\it function ring} of
the underlying space of the quantum world is {\it not} a commutative ring,
and the underlying space itself is not even a point set. \par In spite
of this, the underlying space of the quantum world should be a {\it continuum},
on which one can make a calculus. We hope we can see such mathematics in
the coming century. This article is a survey of such effort or trial to
make such calculus. However, this article does not give a bird-eye-view
of the noncommutative world but this gives several toys which come from
the noncommutative world.

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