The Journal of Geometric Mechanics (JGM)

A note on the Wehrheim-Woodward category

Pages: 507 - 515, Volume 3, Issue 4, December 2011      doi:10.3934/jgm.2011.3.507

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Alan Weinstein - Department of Mathematics, University of California, Berkeley, CA 94720, United States (email)

Abstract: Wehrheim and Woodward have shown how to embed all the canonical relations between symplectic manifolds into a category in which the composition is the usual one when transversality and embedding assumptions are satisfied. A morphism in their category is an equivalence class of composable sequences of canonical relations, with composition given by concatenation. In this note, we show that every such morphism is represented by a sequence consisting of just two relations, one of them a reduction and the other a coreduction.

Keywords:  Symplectic manifold, canonical relation, lagrangian submanifold, categories of relations.
Mathematics Subject Classification:  Primary: 53D12; Secondary: 18B10.

Received: December 2010;      Revised: March 2011;      Available Online: February 2012.