Table of contents

CONTENTS Introduction § 1. Is there such a thing as symplectic topology? § 2. Generalizations of the geometric theorem of Poincaré § 3. Hyperbolic Morse theory § 4. Intersections of Lagrangian manifolds § 5. Legendrian submanifolds of contact manifolds § 6. Lagrangian and Legendrian knots § 7. Two theorems of Givental' on Lagrangian embeddings § 8. Odd-dimensional analogues § 9. Optical Lagrangian manifolds References

CONTENTS § 1. Introduction. Turbulence and resonances § 2. Oscillating self-similar solutions § 3. Cellular structures, multi-jet solutions, strongly coherent structures § 4. Non-uniqueness of asymptotic solutions of the equations for a compressible fluid § 5. The mixed problem (problem with initial and boundary conditions) References

CONTENTS § 1. Sphere coverings and the Hadwiger conjecture § 2. Sphere coverings and the Kneser conjecture § 3. Topology in combinatorial number theory References

CONTENTS § 1. Survey of the subject § 2. Approximate invertibility and a theorem on three-dimensional manifolds § 3. The example of Taylor and its consequences § 4. The theorem of Edwards on the resolvent of a compactum § 5. Widths and homological dimension § 6. Essential maps of spheres with an everywhere dense set of points of univalence § 7. Homological dimension modulo p References

CONTENTS Introduction § 1. Locally homotopy contractible resolutions of sheaves and DG-sheaves § 2. Elements of the homotopy theory of DG-sheaves § 3. Obstruction to a homotopy equivalence of a cochain map of locally homotopy contractible DG-sheaves References

CONTENTS Introduction § 1. Preliminary concepts § 2. The functor D, the predifferential of a fibration § 3. The functor D on the category of A(∞)-algebras § 4. The predifferential of a twisted product References

CONTENTS Introduction § 1. Characterization of n-soft maps of bicompacta § 2. General questions in the theory of covariant functors § 3. Zero-soft and one-soft maps of bicompacta § 4. Non-locally compact absolute extensors § 5. On the properties of maps that are nearly n-soft § 6. The geometry of covariant functors References