Givental's Lagrangian Cone and $S^1$-Equivariant Gromov--Witten Theory

• Autores: Tom Coates
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 15, Nº 1, 2008, págs. 15-31
• Idioma: inglés
• DOI: 10.4310/mrl.2008.v15.n1.a2
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• Resumen

  • In the approach to Gromov--Witten theory developed by Givental, genus-zero Gromov--Witten invariants of a manifold $X$ are encoded by a Lagrangian cone in a certain infinite-dimensional symplectic vector space. We give a construction of this cone, in the spirit of $S^1$-equivariant Floer theory, in terms of $S^1$-equivariant Gromov--Witten theory of $X \times \PP^1$. This gives a conceptual understanding of the ``dilaton shift'': a change-of-variables which plays an essential role in Givental's theory