XXIX Workshop on Geometric Methods in Physics | 27.06-03.07.2010 |

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## Maria Emilia Guimaraes## "DEFORMATION OF COMPLEX STRUCTURES IN TOPOLOGICAL FIELD THEORY"We study a Lie algebra of formal vector eldsWn with it application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. We show that equivalent classes of deformations are describing by a Hochschild cohomology theory of DG-algebra A = (A;Q), Q = @ + @deform, which is dend to be the cohomology of (1)nQ+dHoch. Here @ is the initial non-deformed BRST operator while @deform is the deformed part whose algebra is a Lie algebra of linear vector elds gln. We discuss the identication of the harmonic structure (HT(X);H (X)) of ane space X and the group Extn X(O4;O4) (the HKR isomorphism), and bulk-boundary deformation pairing. |

University of Bialystok |

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