Sheaves and symplectic geometry of cotangent bundles

Introduction
Acknowledgments
Part I. Microlocal theory of sheaves
Chapter I.1. Notations
Chapter I.2. Microsupport
I.2.1. Definition and first properties
I.2.2. Functorial operations
I.2.3. Constructibility
Chapter I.3. Sato's microlocalization
Chapter I.4. Simple sheaves
Chapter I.5. Composition of sheaves
Part II. Sheaves associated with Hamiltonian isotopies
Chapter II.1. Homogeneous case
Chapter II.2. Local behavior
Chapter II.3. Non homogeneous case
Part III. Cut-off lemmas
Chapter III.1. Global cut-off
Chapter III.2. Local cut-off—special case
Chapter III.3. Local cut-off—general case
Chapter III.4. Cut-off and -topology
Chapter III.5. Remarks on projectors—Tamarkin projector
Part IV. Constructible sheaves in dimension 1
Chapter IV.1. Gabriel's theorem
Chapter IV.2. Constructible sheaves on the real line
Chapter IV.3. Constructible sheaves on the circle
Chapter IV.4. Cohomological dimension 1
Part V. Graph selectors
Part VI. The Gromov nonsqueezing theorem
Chapter VI.1. Cut-off in fiber and space directions
Chapter VI.2. Nonsqueezing results
VI.2.1. Invariance of the displacement energy
VI.2.2. Nonsqueezing for a flying saucer
VI.2.3. Nonsqueezing for L0
VI.2.4. Nonsqueezing for the ball
Part VII. The Gromov-Eliashberg theorem
Chapter VII.1. The involutivity theorem
Chapter VII.2. Approximation of symplectic maps
Chapter VII.3. Degree of a continuous map
Chapter VII.4. The Gromov-Eliashberg theorem
Part VIII. The three cusps conjecture
Chapter VIII.1. Examples
Chapter VIII.2. Simple sheaf at a generic tangent point
VIII.2.1. Local cohomology
VIII.2.2. Generic tangent point—notations and hypotheses
VIII.2.3. Local study around C0
Chapter VIII.3. Microlocal linked points
Chapter VIII.4. Examples of microlocal linked points
Chapter VIII.5. Generic tangent point—global study
Chapter VIII.6. Front with one cusp
Chapter VIII.7. Proof of the three cusps conjecture
Chapter VIII.8. The four cusps conjecture
Part IX. Triangulated orbit categories for sheaves
Chapter IX.1. Definition of triangulated orbit categories
Quick reminder on localization
Definition of the orbit category
Internal tensor product and homomorphism
Morphisms in the triangulated orbit category
Direct sums
Direct and inverse images
Chapter IX.2. Microsupport in the triangulated orbit categories
IX.2.1. Definition and first properties
IX.2.2. Functorial behavior
IX.2.3. Microsupport in the zero section
Part X. The Kashiwara-Schapira stack
Chapter X.1. Definition of the Kashiwara-Schapira stack
Link with microlocalization
Chapter X.2. Simple sheaves
Chapter X.3. Obstruction classes
Chapter X.4. The Kashiwara-Schapira stack for orbit categories
Chapter X.5. Microlocal germs
Chapter X.6. Monodromy morphism
Part XI. Convolution and microlocalization
Chapter XI.1. The functor
Chapter XI.2. Adjunction properties
Chapter XI.3. Link with microlocalization
Chapter XI.4. Doubled sheaves
Part XII. Quantization
Chapter XII.1. Quantization for the doubled Legendrian
Chapter XII.2. The triangulated orbit category case
Chapter XII.3. Translation of the microsupport
Chapter XII.4. Restriction at infinity
Part XIII. Exact Lagrangian submanifolds in cotangent bundles
Chapter XIII.1. Fundamental groups
Chapter XIII.2. Vanishing of the Maslov class
Chapter XIII.3. Restriction at infinity
Chapter XIII.4. Vanishing of the second obstruction class
Chapter XIII.5. Homotopy equivalence
Bibliography