18.906: Calendar

18.906 : Calendar

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Tuesday	Thursday
Feb 4 Overview of the course. notes Category Theory. notes [May: Ch 2] pset1 assigned.	Feb 8 Compactly generated weak Hausdorf spaces. notes [May: Ch 5, Steenrod, Strickland]
Feb 11 Pointed spaces and homotopy groups. [May: Ch 8, sec 1, and Ch 9] notes pset2 assigned (due Thurs Feb 20).	Feb 13 Action of fundamental groupoid, weak equivalences, relative homotopy groups, long exact sequence of a pair. notes [May Ch 9, section 5]
Feb 18 = MIT Monday = NO CLASS!	Feb 20 Cofibrations. notes [May: Ch 9, sec 2; Ch 6, sections 1 and 4] pset3 assigned (Due tues Feb 25).-->
Feb 25 Puppe sequences, Fibrations. notes [May: Ch 7, sec 1-4; Ch 9, sec 3-6] pset 4 assigned.	Feb 27 Fiber sequences, Hopf invariant. notes [Hatcher: p346]
Mar 4 Cellular approximation, CW approximation, Whitehead thm. notes [May: Chapter 10, sec 5; Chapter 16, sec 2-3; Chapter 11] pset5 assigned.	Mar 6 Simplicial sets, Homology isos. notes [May: Chapter 15, sec 1]
Mar 11 Homotopy excision notes [Hatcher: p365-369, Appendix 4E, May: Chap 19, sec 4] NOTE: there is NO pset due this week!	Mar 13 Hurewicz theorem, homology whitehead theorem notes [Hatcher: Appedix 4E; Brown]
Mar 18 Brown representability. notes pset7 assigned.	Mar 20 M(pi,n), K(pi,n), Principle G-bundles and classifying spaces [Mitchell] notes
Mar 25 SPRING VACATION	Mar 27 SPRING VACATION
Apr 1 Spectral sequences notes [HatcherSS: p 1-7]	Apr 3 Serre spectral sequence: construction, local coefficients notes [HatcherSS]
Apr 8 Serre spectral sequence: identification of E_2, examples notes [HatcherSS]	Apr 10 Cohomological Serre spectral sequence notes [HatcherSS]
Apr 15 More on classifying spaces notes pset9 assigned.	Apr 17 Chern Classes notes [Milnor and Stasheff: characteristic classes]
Apr 22 PATRIOTS DAY HOLIDAY	Apr 24 Chern classes, cont'd notes pset11 assigned.
Apr 29 Splitting principle, elementary symmetric polynomials	May 1 Thom class and euler classes - Whitney sum pset12 assigned.
May 6 Steenrod operations and Steifel-Whitney classes [Hatcher: appendix on steenrod operations, Milnor-Stasheff]	May 8 Steenrod Operations and Steifel-Whitney classes, cont'd
May 13 Cohomology of BO(n) Unoriented Cobordism theory	May 15 Determination of the unoriented cobordism ring

References

[May]: May, J. P. A concise course in algebraic topology. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 1999.
[Hatcher]: Hatcher, Allen. Algebraic topology. Cambridge University Press, Cambridge, 2002.
[Steenrod]: Steenrod, N. E. A convenient category of topological spaces. Michigan Math. J. 14 1967 133--152.
[Brown]: Brown, Edgar H., Jr. Cohomology theories. Ann. of Math. (2) 75 1962 467--484.
Correction: Brown, Edgar H., Jr. Correction to ``Cohomology theories''. Ann. of Math. (2) 78 1963 201.
[Mitchell]: Mitchell, Steve. Notes on principle bundles and classifying spaces.
[HatcherSS]: Hatcher, Allen. Spectral sequences in algebraic topology.
[Strickland]: Strickland, Neil. The category of CGWH spaces (Note that what I am calling "CG" Strickland calls "CGWH")