The recent revolution in differential topology related to the
discovery of non-standard ("exotic") smoothness structures on
topologically trivial manifolds such as R4 suggests many exciting
opportunities for applications of potentially deep importance for
the spacetime models of theoretical physics, especially general
relativity. This rich panoply of new differentiable structures lies
in the previously unexplored region between topology and geometry.
Just as physical geometry was thought to be trivial before Eintein,
physicists have continued to work under the tacit -- but now shown
to be incorrect -- assumption that differentiability is uniquely
determined by topology for simple four-manifolds. Since
diffeomorphisms are the mathematical models for physical coordinate
transformations, Einstein's relativity principle requires that
these models be physically inequivalent. This book provides an
introductory survey of some of the relevant mathematics and
presents preliminary results and suggestions for further
applications to spacetime models.
General
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