# Geometry of special holonomy and related topics by Naichung Conan Leung; Shing-Tung Yau

By Naichung Conan Leung; Shing-Tung Yau

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Extra resources for Geometry of special holonomy and related topics

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However there is an obvious strategy for removing this restriction. We work with suitable generic perturbations of the Calabi-Yau structure, involving triples ω, ρ, ρ with ω ∧ ρ = 0. It is very reasonable to expect that for generic perturbations of this kind all solutions are regular. But as we explained in Section 3 we have then to give up the assumption that σ is closed, so we get nonzero Fredholm indices for adapted bundles. But this just means that, in the ﬁnite-dimensional analogue, we need to compute twisted cohomology using a 1-form with zeros of diﬀerent indices so we can have a nontrivial chain complex.

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H. SW ⇒ Gr: from the Seiberg-Witten equation to pseudoholomorphic curves Jour. Amer. Math. Soc. 9 845–918 (1996). [35] Taubes, C. H. Nonlinear generalisations of a 3-manifold’s Dirac operator In: Trends in Math. Phys. AMS/IP Studies Adv. Math. 13 475–486 (1998). P. A holomorphic Casson invariant for Calabi-Yau 3-folds and bundles on K3 ﬁbrations Jour. Diﬀerential Geometry 54 367–438 (2000). P. Moment maps, monodromy and mirror manifolds In Symplectic geometry and mirror symmetry, Seoul 2000 World Scientiﬁc 467–498 (2001).