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arXiv · 2312.04477

Conically singular Cayley submanifolds II: Desingularisations

Gilles Englebert
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Abstract

This is the second in a series of three papers working towards constructing fibrations of compact Spin(7) manifolds by Cayley submanifolds. In this paper we show that a conically singular Cayley submanifold in an almost Spin(7)-manifold can be desingularised by gluing in a rescaled asymptotically conical submanifold of $\mathbb{R}^8$ with the same asymptotic cone. We assume that both the conically singular and the asymptotically conical Cayley submanifold are unobstructed in their respective moduli spaces.

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Gilles Englebert. 2023-12-07. Conically singular Cayley submanifolds II: Desingularisations. https://arxiv.org/abs/2312.04477

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