Intersections of quadrics, momentangle manifolds, and Hamiltonianminimal Lagrangian embeddings
Abstract
We study the topology of Hamiltonianminimal Lagrangian submanifolds N in C^m constructed from intersections of real quadrics in a work of the first author. This construction is linked via an embedding criterion to the wellknown Delzant construction of Hamiltonian toric manifolds. We establish the following topological properties of N: every N embeds as a submanifold in the corresponding momentangle manifold Z, and every N is the total space of two different fibrations, one over the torus T^{mn} with fibre a real momentangle manifold R, and another over a quotient of R by a finite group with fibre a torus. These properties are used to produce new examples of Hamiltonianminimal Lagrangian submanifolds with quite complicated topology.
 Publication:

arXiv eprints
 Pub Date:
 March 2011
 DOI:
 10.48550/arXiv.1103.4970
 arXiv:
 arXiv:1103.4970
 Bibcode:
 2011arXiv1103.4970M
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Algebraic Topology;
 Mathematics  Differential Geometry
 EPrint:
 14 pages, published version (minor changes)