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· 제목 : Differential Algebraic Topology (Hardcover) (From Stratifolds to Exotic Spheres)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 위상기하학
· ISBN : 9780821848982
· 쪽수 : 218쪽
· 출판일 : 2010-05-08
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 위상기하학
· ISBN : 9780821848982
· 쪽수 : 218쪽
· 출판일 : 2010-05-08
목차
- Introduction
- A quick introduction to stratifolds
- Smooth manifolds revisited
- Stratifolds
- Stratifolds with boundary: ��-stratifolds
- ℤ/2-homology
- The Mayer-Vietoris sequence and homology groups of spheres
- Brouwer’s fixed point theorem, separation, invariance of dimension
- Homology of some important spaces and the Euler characteristic
- Integral homology and the mapping degree
- A comparison theorem for homology theories and ����-complexes
- Künneth’s theorem
- Some lens spaces and quaternionic generalizations
- Cohomology and Poincaré duality
- Induced maps and the cohomology axioms
- Products in cohomology and the Kronecker pairing
- The signature
- The Euler class
- Chern classes and Stiefel-Whitney classes
- Pontrjagin classes and applications to bordism
- Exotic 7-spheres
- 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
- Bibliography
- Index
