{"paper":{"title":"Symplectic Dirac Operators and Mpc-structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SG","authors_text":"John Rawnsley, Michel Cahen, Simone Gutt","submitted_at":"2011-06-03T08:41:22Z","abstract_excerpt":"Given a symplectic manifold $(M,\\omega)$ admitting a metaplectic structure, and choosing a positive $\\omega$-compatible almost complex structure $J$ and a linear connection $\\nabla$ preserving $\\omega$ and $J$, Katharina and Lutz Habermann have constructed two Dirac operators $D$ and ${\\wt{D}}$ acting on sections of a bundle of symplectic spinors. They have shown that the commutator $[ D, {\\wt{D}}]$ is an elliptic operator preserving an infinite number of finite dimensional subbundles. We extend the construction of symplectic Dirac operators to any symplectic manifold, through the use of $\\Mpc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0588","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}