Math 215b Notes: Algebraic Topology
نویسنده
چکیده
1. Simplices, ∆-Complexes, and Homology: 1/8/15 1 2. Properties of Singular Homology: 1/13/15 4 3. Homotopy Invariance of Singular Homology: 1/15/15 7 4. Applications of Homotopy Invariance and Excision: 1/20/15 10 5. Equivalence of Singular and Simplicial Homology: 1/22/15 14 6. Degrees of Maps on Sn: 1/27/15 17 7. The Mayer-Vietoris Sequence and Applications: 1/29/15 20 8. CW Complexes: 2/3/15 23 9. Some Loose Ends: 2/5/15 27 10. The Lefschetz Fixed-Point Theorem: 2/10/15 30 11. Cohomology and the Universal Coefficient Theorems: 2/12/15 32 12. The Universal Coefficient Theorems: 2/17/15 36 13. The Cup Product: 2/19/15 39 14. Graded Commutativity and a Künneth Formula: 2/24/15 41 15. The Künneth Formula in Cohomology: 2/26/15 43 16. Poincaré Duality: 3/3/15 46 17. Sections and Mayer-Vietoris Induction: 3/5/15 49 18. The Cap Product: 3/10/15 53 19. Proof of Poincaré Duality: 3/12/15 55
منابع مشابه
Math 631 Notes Algebraic Geometry Lectures
1 Algebraic sets, affine varieties, and the Zariski topology 4 1.1 Algebraic sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Hilbert basis theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Zariski topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1 Proof that affine algebraic sets form closed sets on a t...
متن کاملMath 632 Notes Algebraic Geometry
1 Affine schemes 4 1.1 Motivation and review of varieties . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 First attempt at defining an affine scheme . . . . . . . . . . . . . . . . . . . 4 1.3 Affine schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 The Zariski topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 The ringed space s...
متن کاملInternal Topology on MI-groups
An MI-group is an algebraic structure based on a generalization of the concept of a monoid that satisfies the cancellation laws and is endowed with an invertible anti-automorphism representing inversion. In this paper, a topology is defined on an MI-group $G$ under which $G$ is a topological MI-group. Then we will identify open, discrete and compact MI-subgroups. The connected components of th...
متن کاملde Matematica, 1973, 321–327. [5] Chern Classes for Singular Algebraic Varieties, Annals of Math 100 (1974), 423–432. [6] Les Classes Caractéristiques et le Théorème de Riemann-Roch pour les Variétiés Singulières,
[1] Fourier Analysis of Uniform Random Number Generators, with R. R. Coveyou, J. Assoc. Comp. Mach. 14 (1967), 100–119. [2] Singularities of Vector Bundle Maps, Proceedings of Liverpool Singularities Symposium I, Springer Lect. Notes in Math. (1971), 316–318. [3] Generic Vector Bundle Maps, Dynamical Systems, M. Peixoto, ed., Academic Press, 1973, 165–327. [4] Characteristic Classes for Singula...
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