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The Unity of Mathematics pp 457–471Cite as

Symplectomorphism Groups and Quantum Cohomology

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Part of the book series: Progress in Mathematics ((PM,volume 244))

Summary

We discuss the question of what quantum methods (J-holomorphic curves and quantum homology) can tell us about the symplectomorphism group and its compact subgroups. After describing the rather complete information we now have about the case of the product of two 2-spheres, we describe some recent results of McDuff-Tolman concerning the symplectomorphism group of toric manifolds. This leads to an interpretation of the relations in the quantum cohomology ring of a symplectic toric manifold in terms of the Seidel elements of the generating circles of the torus action.

To my teacher, Israel Moiseevich Gelfand, on the occasion of his 90th birthday.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, USA

    Dusa McDuff

Authors
  1. Dusa McDuff
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Pavel Etingof  & I. M. Singer  & 

  2. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Vladimir Retakh

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© 2006 Birkhäuser Boston

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McDuff, D. (2006). Symplectomorphism Groups and Quantum Cohomology. In: Etingof, P., Retakh, V., Singer, I.M. (eds) The Unity of Mathematics. Progress in Mathematics, vol 244. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4467-9_13

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