Getzler, E. Two-dimensional topological gravity and equivariant cohomology. (English) Zbl 0806.53073 Commun. Math. Phys. 163, No. 3, 473-489 (1994). The first part of the paper makes precise the analogy between topological string theory and equivariant cohomology for differentiable actions of the circle group on manifolds. It is shown that topological string theory is the “derived functor” of semi-relative cohomology, just as equivariant cohomology is the derived functor of basic cohomology. The second part describes an algebraic structure on the equivariant cohomology of a topological conformal field theory that is analogous to the Batalin-Vilkovisky algebra that was shown to be associated with the basic cohomology of the same type of theory by the same author. That algebraic structure, called a gravity algebra, is a certain generalization of a Lie algebra with an infinite sequence of operations satisfying quadratic relations generalizing the Jacobi rule. Reviewer: H.Rumpf (Wien) Cited in 6 ReviewsCited in 30 Documents MSC: 53Z05 Applications of differential geometry to physics 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Keywords:topological string theory; semi-relative cohomology; conformal field theory PDFBibTeX XMLCite \textit{E. Getzler}, Commun. Math. Phys. 163, No. 3, 473--489 (1994; Zbl 0806.53073) Full Text: DOI arXiv References: [1] Arnold, V.I.: The cohomology ring of the colored braid group. Mat. Zametki5, 227–231 (1969) [2] Atiyah, M.F., Bott, R.: The moment map and equivariant cohomology. Topology23, 1–28 (1994) · Zbl 0521.58025 [3] Bershadsky, M., Lerche, W., Nemeschansky, D., Warner, N.P.: ExtendedN=2 superconformal structure of gravity andW-gravity coupled to matter. hep-th/9211040 [4] Eguchi, T., Kanno, H., Yamada, Y., Yang, S.-K.: Topological strings, flat coordinates and gravitational descendants. University of Tokyo preprint UT-630. hep-th/9302048 [5] Feigin, B., Frenkel, E.: Semi-infinite Weil complex and the Virasoro algebra. Commun. Math. Phys.137, 617–639 (1991) · Zbl 0726.17035 [6] Friedan, D., Martinec, E., Shenker, S.: Conformal invariance, supersymmetry and string theory. Nucl. Phys.B271, 93–165 (1986) [7] Getzler, E.: Batalin-Vilkovisky algebras and two-dimensional topological field theories hep-th/9212043, to appear, Commun. Math. Phys. · Zbl 0807.17026 [8] Getzler, E., Jones, J.D.S.: Operads, homotopy algebra, and iterated integrals for double loop spaces. Preprint. [9] Ginzburg, V.A., Kapranov, M.M.: Koszul duality for operads. Preprint, 1993 · Zbl 0855.18006 [10] Jones, J.D.S.: Cyclic homology and equivariant homology. Topology24, 187–215 (1985) · Zbl 0569.16021 [11] Witten, E.: On the structure of the topological phase of two-dimensional gravity. Nucl. Phys.B340, 281–332 (1990) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.