ANISOTROPIC NULL STRING COSMOLOGIES

We study string propagation in an anisotropic, cosmological background. We solve the equations of motion and the constraints by performing a perturbative expansion of the string coordinates in powers if c2 — the worldsheet speed of light. To zeroth order the string is approximated by a tensionless string (since c is proportional to the string tension T). We obtain exact, analytical expressions for the zeroth- and first-order solutions and we discuss some cosmological implications.

On a Stringy Singular Cohomology

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 L2-cohomology, but is markedly different in some aspects. For one, unlike the intersection (co)homology and the L2-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.