A gluing theorem for ACyl associative submanifolds produces closed rigid associatives in twisted connected sum G2-manifolds with topologies S^3, RP^3 and RP^3#RP^3.
Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary
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abstract
McLean proved that the moduli space of coassociative deformations of a compact coassociative 4-submanifold C in a G_2-manifold (M,phi,g) is a smooth manifold of dimension equal to b^2_+(C). In this paper, we show that the moduli space of coassociative deformations of a noncompact, asymptotically cylindrical coassociative 4-fold C in an asymptotically cylindrical G_2-manifold (M,phi,g) is also a smooth manifold. Its dimension is the dimension of the positive subspace of the image of H^2_cs(C,R) in H^2(C,R).
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Associative submanifolds in twisted connected sum $G_2$-manifolds
A gluing theorem for ACyl associative submanifolds produces closed rigid associatives in twisted connected sum G2-manifolds with topologies S^3, RP^3 and RP^3#RP^3.