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Deformation theory of asymptotically conical coassociative 4‐folds
Author(s) -
Lotay Jason D.
Publication year - 2009
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdp006
Subject(s) - moduli space , mathematics , conical surface , dimension (graph theory) , pure mathematics , mathematical analysis , moduli , cone (formal languages) , space (punctuation) , planar , manifold (fluid mechanics) , zero (linguistics) , kernel (algebra) , geometry , physics , quantum mechanics , algorithm , computer science , mechanical engineering , linguistics , philosophy , computer graphics (images) , engineering , operating system
Suppose that a coassociative 4‐fold N in ℝ 7 is asymptotically conical (AC) to a cone C with rate λ < 1. If λ ∈ [−2, 1) is generic, then we show that the moduli space of coassociative deformations of N that are also AC to C with rate λ is a smooth manifold, and we calculate its dimension. If λ < − 2 and generic, then we show that the moduli space is locally homeomorphic to the kernel of a smooth map between smooth manifolds, and we give a lower bound for its expected dimension. We also derive a test for when N will be planar if λ < − 2 and we discuss examples of AC coassociative 4‐folds.