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A note on the Wehrheim-Woodward category

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  • 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.
    Mathematics Subject Classification: Primary: 53D12; Secondary: 18B10.


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    M. M. Cohen, "A Course in Simple-Homotopy Theory,'' Graduate Texts in Mathematics, 10, Springer-Verlag, New York-Berlin, 1973.


    J. Rognes, Lecture notes on algebraic k-theory, April 29, 2010. Available from: http://folk.uio.no/rognes/kurs/mat9570v10/akt.pdf.


    K. Wehrheim and C. T. Woodward, Functoriality for Lagrangian correspondences in Floer theory, Quantum Topology, 1 (2010), 129-170.doi: 10.4171/QT/4.

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