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arXiv · 2508.01899

Deformations of asymptotically cylindrical associative submanifolds

Gorapada Bera
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Abstract

This article develops the deformation theory of asymptotically cylindrical (ACyl) associative submanifolds in ACyl $G_2$-manifolds, laying the foundation for the gluing of ACyl associative submanifolds in twisted connected sum $G_2$-manifolds presented by the author in [Ber22]. We study the moduli space of ACyl associative submanifolds with a fixed asymptotic holomorphic curve and a fixed rate, as well as the moduli space where this asymptotic data is allowed to vary, each endowed with a natural topology. We also express their virtual dimensions in terms of data on the asymptotic cross-sections.

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Gorapada Bera. 2025-08-03. Deformations of asymptotically cylindrical associative submanifolds. https://arxiv.org/abs/2508.01899

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