On A Stringy Singular Cohomology

Details On A Stringy Singular Cohomology On A Stringy Singular Cohomology

1996-12-06

arxiv.org/abs/hep-th/9612075v1

Mod.Phys.Lett. A12 (1997) 521-534

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, TeX + harvmac, no figures

Scientific paper

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.

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