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Differential Algebraic Topology: From Stratifolds to Exotic Spheres
About this Title
Matthias Kreck, Hausdorff Research Institute for Mathematics, Bonn, Germany
Publication: Graduate Studies in Mathematics
Publication Year:
2010; Volume 110
ISBNs: 978-0-8218-4898-2 (print); 978-1-4704-1592-1 (online)
DOI: https://doi.org/10.1090/gsm/110
MathSciNet review: MR2641092
MSC: Primary 55-01; Secondary 55R40, 57-01, 57R20, 57R55
Table of Contents
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Front/Back Matter
Chapters
- Chapter 0. A quick introduction to stratifolds
- Chapter 1. Smooth manifolds revisited
- Chapter 2. Stratifolds
- Chapter 3. Stratifolds with boundary: $c$-stratifolds
- Chapter 4. $\mathbb {Z}$/2-homology
- Chapter 5. The Mayer-Vietoris sequence and homology groups of spheres
- Chapter 6. Brouwer’s fixed point theorem, separation, invariance of dimension
- Chapter 7. Homology of some important spaces and the Euler characteristic
- Chapter 8. Integral homology and the mapping degree
- Chapter 9. A comparison theorem for homology theories and $CW$-complexes
- Chapter 10. Künneth’s theorem
- Chapter 11. Some lens spaces and quaternionic generalizations
- Chapter 12. Cohomology and Poincaré duality
- Chapter 13. Induced maps and the cohomology axioms
- Chapter 14. Products in cohomology and the Kronecker pairing
- Chapter 15. The signature
- Chapter 16. The Euler class
- Chapter 17. Chern classes and Stiefel-Whitney classes
- Chapter 18. Pontrjagin classes and applications to bordism
- Chapter 19. Exotic 7-spheres
- Chapter 20. Relation to ordinary singular (co)homology
- Appendix A. Constructions of stratifolds
- Appendix B. The detailed proof of the Mayer-Vietoris sequence
- Appendix C. The tensor product