Zero-loop open strings in the cotangent bundle and Morse homotopy.(English)Zbl 0938.32009

The authors prove that the rational homotopy type of a compact manifold $$M$$ can be described by the moduli space of pseudo-holomorphic discs with appropriate Lagrangian boundary conditions in its cotangent bundle $$T^*M$$. For this, two moduli spaces are investigated. These are the moduli space of graph flows, which represents the Morse theory side, and the moduli space of pseudo-holomorphic discs, which is related to symplectic geometry. The main theorem asserts their equivalence.

MSC:

 32G13 Complex-analytic moduli problems
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