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Floer trajectories with immersed nodes and scale-dependent gluing

Floer trajectories with immersed nodes and scale-dependent gluing

Development of pseudo-holomorphic curves and Floer homology in symplectic topology has led to moduli spaces of pseudo-holomorphic curves consisting of both "smooth elements" and "spiked elements", where the latter are combinations of J -holomorphic curves (or Floer trajectories) and gradient flow line segments.In many cases the "spiked elements" naturally arise …