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- W1560757553 abstract "On a symplectic manifold $M$, the quantum product defines a complex, one parameter family of flat connections called the A-model or Dubrovin connections. Let $hbar$ denote the parameter. Associated to them is the quantum $mathcal{D}$ - module ${mathcal{D}}/I$ over the Heisenberg algebra of first order differential operators on a complex torus. An element of $I$ gives a relation in the quantum cohomology of $M$ by taking the limit as $hbarto 0$. Givental (HomGeom), discovered that there should be a structure of a $mathcal{D}$ - module on the (as yet not rigorously defined) ${S^1}$ equivariant Floer cohomology of the loop space of $M$ and conjectured that the two modules should be equal. Based on that, we formulate a conjecture about how to compute the quantum cohomology $mathcal{D}$ - module in terms of Morse theoretic data for the symplectic action functional. The conjecture is proven in the case of toric manifolds with $int_d{c_1}> 0$ for all nonzero classes $d$ of rational curves in $M$." @default.
- W1560757553 created "2016-06-24" @default.
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- W1560757553 date "2002-03-08" @default.
- W1560757553 modified "2023-09-27" @default.
- W1560757553 title "Quantum Cohomology and Morse Theory on the Loop Space of Toric Varieties" @default.
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