Zero-loop open strings in the cotangent bundle and Morse homotopy

TL;DRAbstract

Introduction. Many important works in symplectic geometry and topology are regarded as the symplectization or the quantization of the corresponding results in ordinary geometry and topology. One outstanding example is the celebrated Arnold conjecture which concerns the number of fixed points of a symplectic diffeomorphism or that of intersection points of two Lagrangian submanifolds. The homological version of the conjecture has been proved in various cases (see , The estimate (in its homological version) predicted by the Arnold conjecture can be regarded as the symplectization or the quantization of the Morse inequality, and conversely the latter can be considered as the semi-classical limit and so a consequence of the former. From now on, we will use the term "quantization" for the similar process that appear below.

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