Asymptotically Conical Associative 3-folds

Details Asymptotically Conical Associative 3-folds Asymptotically Conical Associative 3-folds

2008-02-24

arxiv.org/abs/0802.3536v2

Q J Math, Advance Access published on November 12, 2009

Mathematics

Differential Geometry

33 pages, v2: major changes for published version, mainly regarding the twisted Dirac and d-bar operators

Scientific paper

10.1093/qmath/hap036

Given an associative 3-fold in R^7 which is asymptotically conical with generic rate less than 1, we show that its moduli space of deformations is locally homeomorphic to the kernel of a smooth map between smooth manifolds. Moreover, the virtual dimension of the moduli space is computed and shown to be non-negative for rates greater than -1, whereas the associative 3-fold is expected to be isolated for rates less than or equal to -1.

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