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3. Symplectic geometry


    1. Add remark

      Problem 3.1.

      Can the "looking glass" parallel/analogy between rational homotopy theory (= symplectic geometry of cotangent bundles) and local ring theory be generalized/ further exploited to other symplectic manifolds (e.g. Weinstein manifolds)?

      A)
      • $\bullet$ can "attach handles" to Weinstein manifolds
      • $\bullet$ there exists a natural "categorical compactification" of Fukaya categories via "stop" or "Lefschetz fibrations"
      B)
      • $\bullet$ Can rational homotopy theory e.g. Sullivan minimal models can be used to e.g. construct resolutions?
      Comment: The initial parallel comes from $$C_*(\Omega_q M)=Ext_{C^{\bullet}M}(k,k)=A$$ where $$C_*(\Omega_q M)\simeq End_{Fuk(T^*M)}(T^*_q M, T^*_q M)$$ (Here $M$ is assumed to be simply connected).

          Cite this as: AimPL: Syzygies and mirror symmetry, available at http://aimpl.org/syzygyms.