Arithmetic and Geometry Around Quantization (Progress in Mathematics)

Several of these examples are further described as fibrations over the Eguchi-Hanson gravitational instanton and, to the best of our knowledge, have not been previously considered in the literature.

Calibrated associative and Cayley embeddings. Using the Cartan-Kahler theory, and results on real algebraic structures, we prove two embedding theorems. Second, the interior of a smooth, compact 4-manifold K, whose double has a trivial bundle of self-dual 2-forms, may be isometrically embedded into a Spin 7 -manifold as a Cayley submanifold.

Along the way, we also show that Bochner's Theorem on real analytic approximation of smooth differential forms, can be obtained using real algebraic tools developed by Akbulut and King. These forms can then be used to define various different complex and symplectic structures on certain 6-dimensional subbundles of T M. When these bundles are integrated they give mirror CY manifolds. We thus propose that the mirror of a Joyce space of the first kind will be another Joyce space of the first kind.

As a spin-off we conclude from this analysis that no 5-brane instantons are present in compactifications of eleven dimensional supergravity over Joyce manifolds of the first kind. We believe the approach here makes things easier and keeps the presentation elementary.

This paper is essentially self contained. In order to prove this we used the powerful tools of Fredholm Theory for noncompact manifolds which was developed by Lockhart and McOwen and independently by Melrose.

In this paper, we extend this result to the moving boundary case. Let F be a small open neighbourhood of 0 in ker Phi.

Calibrated Manifolds and Gauge Theory. The purpose of this paper is to relate the geometries of calibrated submanifolds to their gauge theories. We show that deformation spaces can be perturbed to be smooth and finite dimensional. We also get similar results for the deformation spaces of other calibrated submanifolds. On the geometry of multisymplectic manifolds - Cantrijn, F. On the Geometry of Closed G2-Structures An example of a compact calibrated manifold associated with the exceptional Lie group G2.

Damien Calaque

A family of compact solvable G2-calibrated manifolds, Tohoku Math. J 2 39, , no. Riemannian manifolds with structure group G2, Ann. New examples of Riemannian manifolds with structure group G2, Rend. Topology of character varieties and representations of quivers , Comptes Rendus Mathematique , Volume , Issues , February , Pages doi: Arithmetic harmonic analysis on character and quiver varieties , Duke Mathematical Journal , Volume , Number 2 , , arXiv: Mixed Hodge polynomials of character varieties , Inventiones Mathematicae , , no.

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Betti numbers of holomorphic symplectic quotients via arithmetic Fourier transform , Proceedings of the National Academy of Sciences of the United States of America , no. Progress in Mathematics, Vol. On Yang-Mills-instantons on multi-centered metrics , arXiv: Hodge cohomology of gravitational instantons , Duke Mathematical Journal , Issue 3, , arXiv: Toric hyperkaehler varieties , Documenta Mathematica , 7 , , arXiv: