| Tuesday | Thursday |
|---|---|
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Feb 5 Overview of the course. notes Category Theory. notes [May: Ch 2] pset1 assigned. |
Feb 7 No class Read: Compactly generated weak Hausdorf spaces. notes [May: Ch 5, Steenrod, Strickland] |
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Feb 12 Pointed spaces and homotopy groups. [May: Ch 8, sec 1, and Ch 9] notes pset2 assigned (due Thurs Feb 21). |
Feb 14 No class Read: Action of fundamental groupoid, weak equivalences, relative homotopy groups, long exact sequence of a pair. notes [May Ch 9, section 5] |
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Feb 19 = MIT Monday = NO CLASS! |
Feb 21 Cofibrations. notes [May: Ch 9, sec 2; Ch 6, sections 1 and 4] pset3 assigned (Due tues Feb 26). |
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Feb 26 Puppe sequences, Fibrations. notes [May: Ch 7, sec 1-4; Ch 9, sec 3-6] pset 4 assigned. |
Feb 28 Fiber sequences, Hopf invariant. notes [Hatcher: p346] |
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Mar 5 Cellular approximation, CW approximation, Whitehead thm. notes [May: Chapter 10, sec 5; Chapter 16, sec 2-3; Chapter 11] |
Mar 7 Simplicial sets, Homology isos, Homotopy excision. notes [May: Chapter 15, sec 1] |
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WEDNESDAY, Mar 13 Homotopy excision, Hurwitz thm, homology whitehead notes [Hatcher: p365-369, Appendix 4E, May: Chap 19, sec 4] pset6 assigned. |
Mar 14 Brown representability, notes [Hatcher: Appedix 4E; Brown] |
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Mar 19 Proof of Brown representability. M(pi,n), K(pi,n) notes pset7 assigned. |
Mar 21 Principle G-bundles and classifying spaces [Mitchell] notes |
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Mar 26 SPRING VACATION |
Mar 28 SPRING VACATION |
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Apr 2 Spectral sequences notes [HatcherSS: p 1-7] pset8 assigned. |
Apr 4 Serre spectral sequence: construction, local coefficients notes [HatcherSS] |
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Apr 9 Serre spectral sequence: identification of E_2, examples notes [HatcherSS] pset9 assigned. |
Apr 11 Cohomological Serre spectral sequence notes [HatcherSS] |
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Apr 16 PATRIOTS DAY HOLIDAY |
Apr 18 More on classifying spaces notes pset10 assigned. |
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Apr 23 Chern Classes (Guest lecturer: Haynes Miller) my notes Miller's notes [Milnor and Stasheff: characteristic classes] pset11 assigned. |
Apr 25 Chern classes, cont'd (Guest lecturer: Haynes Miller) my notes Miller's notes |
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Apr 30 Splitting principle, elementary symmetric polynomials notes pset12i assigned. (most will need thurs lecture). |
May 2 Thom class and euler classes - Whitney sum notes |
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May 7 Steenrod operations and Steifel-Whitney classes notes [Hatcher: appendix on steenrod operations, Milnor-Stasheff] pset 13 assigned. |
May 9 Steenrod Operations and Steifel-Whitney classes, cont'd notes |
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May 14 Cohomology of BO(n) Unoriented Cobordism theory |
May 16 Determination of the unoriented cobordism ring |