  String theory has already motivated, suggested, and sometimes well-nigh
proved a number of interesting and sometimes unexpected mathematical results,
such as mirror symmetry. A careful examination of the behavior of string
propagation on (mildly) singular varieties similarly suggests a new type of
(co)homology theory. It has the `good behavior' of the well established
intersection (co)homology and $L^2$-cohomology, but is markedly different in
some aspects. For one, unlike the intersection (co)homology and the
$L^2$-cohomology (or any other known thus far), this new cohomology is
symmetric with respect to the mirror map. Among the available choices, this
makes it into a prime candidate for describing the string theory zero modes in
geometrical terms.
