Introduction 2. Notation, comments and acknowledgements 3. Reminders on the singular support of sheaves 4. Quantization of Hamiltonian isotopies 5. Spectral invariants for sheaves and Lagrangians 5.1. Definition of spectral invariants 5.2. The case of Hamiltonian maps 5.3. Defining γ-coisotropic subsets 6. The γ g-metric on sheaves 6.1. The γ g-topology 6.2. Link with spectral invariants 6.3. γ g-limits and colimits 7. Proof of Theorem 1.2 8. γ-coisotropic vs cone-coisotropic 8.1. A γ-coisotropic set is cone-coisotropic 8.2. A cone-coisotropic set that is not γ-coisotropic 9. Questions and comments Appendix A. Persistence modules and Barcodes Appendix B. Decomposition in the completion of D l c (R) B.1. Limits of constructible sheaves B.2. Decomposition in D l c (R) Appendix C. Comparing different interleaving metrics on D(N × R). Appendix D. Local Floer cohomology