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Deformations and gluing of asymptotically cylindrical manifolds with exceptional holonomy 10.17863/CAM.16204 Nordström, Johannes In Berger's classification of Riemannian holonomy groups there are several infinite families and two exceptional cases: the groups Spin(7) and G_2. This thesis is mainly concerned with 7-dimensional manifolds with holonomy G_2. A metric with holonomy contained in G_2 can be defined in terms of a torsion-free G_2-structure, and a G_2-manifold is a 7-dimensional manifold equipped with such a structure. There are two known constructions of compact manifolds with holonomy exactly G_2. Joyce found examples by resolving singularities of quotients of flat tori. Later Kovalev found different examples by gluing pairs of exponentially asymptotically cylindrical (EAC) G_2-manifolds (not necessarily with holonomy exactly G_2) whose cylinders match. The result of this gluing construction can be regarded as a generalised connected sum of the EAC components, and has a long approximately cylindrical neck region. We consider the deformation theory of EAC G_2-manifolds and show, generalising from the compact case, that there is a smooth moduli space of torsion-free EAC G_2-structures. As an application we study the deformations of the gluing construction for compact G_2-manifolds, and find that the glued torsion-free G_2-structures form an open subset of the moduli space on the compact connected sum. For a fixed pair of matching EAC G_2-manifolds the gluing construction provides a path of torsion-free G_2-structures on the connected sum with increasing neck length. Intuitively this defines a boundary point for the moduli space on the connected sum, representing a way to `pull apart' the compact G_2-manifold into a pair of EAC components. We use the deformation theory to make this more precise. We then consider the problem whether compact G_2-manifolds constructed by Joyce's method can be deformed to the result of a gluing construction. By proving a result for resolving singularities of EAC G_2-manifolds we show that some of Joyce's examples can be pulled apart in the above sense. Some of the EAC G_2-manifolds that arise this way satisfy a necessary and sufficient topological condition for having holonomy exactly G_2. We prove also deformation results for EAC Spin(7)-manifolds, i.e. dimension 8 manifolds with holonomy contained in Spin(7). On such manifolds there is a smooth moduli space of torsion-free EAC Spin(7)-structures. Generalising a result of Wang for compact manifolds we show that for EAC G_2-manifolds and Spin(7)-manifolds the special holonomy metrics form an open subset of the set of Ricci-flat metrics. University of Cambridge 2008-10-14T14:12:43Z Thesis Doctoral Doctor of Philosophy (PhD) en This work was supported by the EPSRC and the Gates Cambridge Trust. http://www.dspace.cam.ac.uk/handle/1810/214782 https://www.repository.cam.ac.uk/handle/1810/214782 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/7f72b9db-bae3-4a4e-a35c-158f56da2583/download 828538518210774b59ddd5bc3be9db4e https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/be4a5004-a71e-4e11-b37a-b1757eef70e7/download 583673b5361970759d2e34a24f17330f https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/17b23118-9f6f-45b2-a07c-b6b61cd29556/download c6c9e4ec13c4e904cc0709778e585e27 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/4dcba81e-32ad-4b14-ae87-223eec143009/download bf8f949e0ddbd16c3bead9a5e76ed08f https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/93e6913a-09ec-42ea-aac4-b5fb0904f5f5/download 85afc0225ea73fb71a165b09f5713f5c https://www.rioxx.net/licenses/all-rights-reserved/ differential geometry special holonomy