Topological conformal field theories and Calabi-Yau categories |
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Authors: | Kevin Costello |
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Institution: | Department of Mathematics, Imperial College London, UK |
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Abstract: | This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These Gromov-Witten type invariants depend on a Calabi-Yau A∞ category, which plays the role of the target in ordinary Gromov-Witten theory. When we use an appropriate A∞ version of the derived category of coherent sheaves on a Calabi-Yau variety, this constructs the B model at all genera. When the Fukaya category of a compact symplectic manifold X is used, it is shown, under certain assumptions, that the usual Gromov-Witten invariants are recovered. The assumptions are that open-closed Gromov-Witten theory can be constructed for X, and that the natural map from the Hochschild homology of the Fukaya category of X to the ordinary homology of X is an isomorphism. |
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Keywords: | Topological conformal field theories Moduli spaces of surfaces A-infinity categories |
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