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In order to '''regularize''' the [[moduli spaces of pseudoholomorphic polygons]] <ma In order to obtain boundary stratifications which imply the <math>A_\infty</math>-re

...ified Morse trajectory spaces]] <math>\overline\mathcal{M}(x_i,L_i)</math> inherit a natural smooth structure (see [https://arxiv.org/abs/1205.0713]). 1. <math>T</math> is an ordered tree with sets of vertices <math>V=V^m \cup V^c</math> and edges <m