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Introduction to the $h$-Principle
About this Title
Y. Eliashberg, Stanford University, Stanford, CA and N. Mishachev, Lipetsk Technical University, Lipetsk, Russia
Publication: Graduate Studies in Mathematics
Publication Year:
2002; Volume 48
ISBNs: 978-0-8218-3227-1 (print); 978-1-4704-1796-3 (online)
DOI: https://doi.org/10.1090/gsm/048
MathSciNet review: MR1909245
MSC: Primary 53D99; Secondary 57R17, 58E99
Table of Contents
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Front/Back Matter
Chapters
Part 1. Holonomic approximation
- Chapter 1. Jets and holonomy
- Chapter 2. Thom transversality theorem
- Chapter 3. Holonomic approximation
- Chapter 4. Applications
Part 2. Differential relations and Gromov’s $h$-principle
- Chapter 5. Differential relations
- Chapter 6. Homotopy principle
- Chapter 7. Open Diff $V$-invariant differential relations
- Chapter 8. Applications to closed manifolds
Part 3. The homotopy principle in symplectic geometry
- Chapter 9. Symplectic and contact basics
- Chapter 10. Symplectic and contact structures on open manifolds
- Chapter 11. Symplectic and contact structures on closed manifolds
- Chapter 12. Embeddings into symplectic and contact manifolds
- Chapter 13. Microflexibility and holonomic $\mathcal {R}$-approximation
- Chapter 14. First applications of microflexibility
- Chapter 15. Microflexible $\mathfrak {U}$-invariant differential relations
- Chapter 16. Further applications to symplectic geometry
Part 4. Convex integration
- Chapter 17. One-dimensional convex integration
- Chapter 18. Homotopy principle for ample differential relations
- Chapter 19. Directed immersions and embeddings
- Chapter 20. First order linear differential operators
- Chapter 21. Nash-Kuiper theorem