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Are there any contexts in which we can say with certainity that the connected sum of two special holonomy manifolds (eg Kahler, Calabi-Yau, G2...) has the same holonomy group? I would also be interested in such results for weaker structures such as complex structures or torsion-free G-Structures

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    $\begingroup$ How are you doing the connected sum in the Riemannian (or hermitian) category? Topologically, it's well-defined, but ... $\endgroup$ – Ted Shifrin May 31 '19 at 23:55
  • $\begingroup$ I was referring to the riemannian category, although I know there is not a canonical way to do the connected sum in that case. I was just wondering if there has been any work done considering connected sums of special holonomy manifolds in any sense $\endgroup$ – Canonical Momenta Jun 7 '19 at 8:00

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