Deformation theory of asymptotically conical coassociative 4‐folds | Zendy

Lotay Jason D. | Zendy

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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.

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