| Tuesday | Thursday |
|---|---|
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Feb 2 Overview of the course. notes Category Theory. notes [May: Ch 2] pset1 assigned. |
Feb 4 Compactly generated weak Hausdorf spaces. notes [May: Ch 5, Steenrod] |
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Feb 9 Pointed spaces and homotopy groups. [May: Ch 8, sec 1, and Ch 9]notes pset2 assigned. |
Feb 11 Computations of homotopy groups, action of fundamental groupoid, weak equivalences. notes [May Ch 9, sections 4-5] |
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Feb 16 = MIT Monday = NO CLASS! |
Feb 18 Relative homotopy groups, LES of a pair, cofibrations. notes [May: Ch 9, sec 2; Ch 6, sections 1 and 4] pset3 assigned. |
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Feb 23 Puppe sequences, fibrations, LES of a fibration. notes [May: Ch 7, sec 1-4; Ch 9, sec 3-6] pset4 assigned. |
Feb 25 Whitehead theorem. notes [Hatcher: p346] |
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Mar 2 Cellular approximation, homology equivalences, homotopy excision. notes [May: Chapter 10, sec 5; Chapter 16, sec 2-3; Chapter 11] pset5 assigned. |
Mar 4 Hurewicz theorem, homology whitehead theorem. notes [May: Chapter 15, sec 1; Hatcher: p365-369] |
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Mar 9 Brown Representability Theorem, lim^1 notes [Hatcher: Appendix 4E, May: Chap 19, sec 4] pset6 assigned. |
Mar 11 Proof of Brown representability, M(pi,n), K(pi,n) notes [Hatcher: Appedix 4E; Brown] |
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Mar 16 Principle G-bundles and classifying spaces notes [Mitchell] pset7 assigned. |
Mar 18 Principle G-bundles and classifying spaces: cont'd notes |
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Mar 23 SPRING VACATION |
Mar 25 SPRING VACATION |
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Mar 30 Spectral sequences notes [HatcherSS: p 1-7] pset8 assigned. |
Apr 1 Serre spectral sequence: construction notes [HatcherSS] |
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Apr 6 Serre spectral sequence: examples notes [HatcherSS] pset9 assigned. |
Apr 8 Cohomological Serre spectral sequence notes [HatcherSS] |
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Apr 13 Other applications of SSS, change of group notes pset10 assigned. |
Apr 15 Chern Classes notes [Milnor and Stasheff: characteristic classes] |
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Apr 20 PATRIOTS DAY HOLIDAY |
Apr 22 Splitting principle and elementary symmetric polynomials notes pset11 assigned. |
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Apr 27 Cartan up to a constant - Thom Isomorphism - Euler class 21 pset12 assigned. |
Apr 29 Thom class and euler classes - Cartan 22 |
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May 4 Steenrod operations and Steifel-Whitney classes notes [Hatcher: appendix on steenrod operations, Milnor-Stasheff] pset 13 assigned. |
May 6 Steenrod Operations and Steifel-Whitney classes, cont'd notes |
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May 11 Cohomology opf BO(k), Unoriented Cobordism theory notes |
May 13 Determination of the unoriented cobordism ring notes |