Pré-Publication, Document De Travail Année : 2008

Deformations of associative submanifolds with boundary

Damien Gayet

Résumé

Let M be a compact smooth manifold of holonomy G_2. We prove that the space of infinitesimal associative deformations of a compact associative submanifold Y with boundary in a coassociative submanifold X is the solution space of an elliptic problem. Further, we compute its virtual dimension. For \partial Y connected it is given by \int_{\partial Y}c_1(\nu_X)+1-g, where g denotes the genus of \partial Y, \nu_X the orthogonal complement of T\partial Y in TX_{|\partial Y} and c_1(\nu_X) the first Chern class of \nu_X with respect to its natural complex structure.

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Dates et versions

hal-00258055 , version 1 (21-02-2008)
hal-00258055 , version 2 (25-02-2008)

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  • HAL Id : hal-00258055 , version 1

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Damien Gayet, Frederik Witt. Deformations of associative submanifolds with boundary. 2008. ⟨hal-00258055v1⟩

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