Microlocal study of sheaves. II: Constructible sheaves (Q799849)

[Part I appeared ibid. 349-351 (1983; Zbl 0548.58039).] On a real (resp. complex) analytic manifold X, we prove that a complex of sheaves is constructible if and only if it satisfies some finiteness property and if its micro-support [the authors, C. R. Acad. Sci., Paris, Sér. I 295, 487-490 (1982; Zbl 0501.58006)] is a subanalytic (resp. complex analytic) Lagrangian set. Thus we may study the functorial properties, including contact transformations, with our previous results on the micro-support of sheaves. As an application we give a direct image theorem for regular holonomic modules in the non proper case.