18.915 | Fall 2014 | Graduate

Graduate Topology Seminar: Kan Seminar

Reading List

List of Possible Papers

Serre, J. -P. “Cohomologie modulo 2 des complexes d’Eilenberg-Maclane.” Commentarii Mathematici Helvetici 27, no. 1 (1953): 198–232.

Thom, R. “Quelques propriétés globales des variétés différentiables.” Commentarii Mathematici Helvetici 28 (1954): 17–86.

Milnor, J. W. “On the Construction FK.” In Algebraic Topology: A Student’s Guide (London Mathematical Society Lecture Note). Vol. 4. Cambridge University Press, 1972, pp. 119–36. ISBN: 9780521080767.

———. “On Manifolds Homeomorphic to the 7–sphere.” Annals of Mathematics 64, no. 2 (1956): 399–405.

Milnor, J. W., and J. D. Stasheff. Characteristic Classes (Annals of Mathematics Studies). Vol. 76_._ Princeton University Press, 1974. ISBN: 9780691081229. [Preview with Google Books]

Milnor, J. W. “The Geometric Realization of a Semi–simplicial Complex.” Annals of Mathematics 65, no. 2 (1957): 357–62.

Moore, J. C. “Semi-simplicial complexes and Postnikov systems.” In Symposium Internacional de Topologia Algebraica. La Universidad Nacional Autonoma de Mexico y la UNESCO, 1958, pp. 232–47.

Bott, R. “The stable Homotopy Groups of the Classical Groups.” Annals of Mathematics 70, no. 2 (1959): 313–37.

Adams, J. F. “On the Non-existence of Elements of Hopf Invariant One.” Annals of Mathematics 72, no. 1 (1960): 20–104.

———. “Vector Fields on Spheres.” Annals of Mathematics 75, no. 3 (1962): 603–32.

Brown, E. H., Jr.  “Cohomology Theories.” Annals of Mathematics 75, no. 3 (1962): 467–84.

Kervaire, M. A., and J. W. Milnor. “Groups of Homotopy Spheres: I.” Annals of Mathematics 77, no. 3 (1963): 504–37.

Atiyah, M. F. K–theory (Advanced Book Classics). 2nd ed. Notes by D. W. Anderson. Addison Wesley Longman Publishing Company, 1989. ISBN: 9780201093940.

Wall, C. T. C. “Finiteness Conditions for CW–complexes.” Annals of Mathematics 81, no. 1 (1965): 56–69.

Adams, J. F. “On the Groups J (X)–IV.” Topology 5, no. 1 (1966): 21–71.

Adams, J. F., and M. F. Atiyah. “K–theory and the Hopf Invariant.” The Quarterly Journal of Mathematics 17, no. 1 (1966): 31–38.

Quillen, D. G. Homotopical Algebra (Lecture Notes in Mathematics). Vol. 43. Springer, 1967. ISBN: 9783540039143.

Segal, G. “Classifying Spaces and Spectral Sequences.” Publications Math´ematiques de I’lnstitut Hautes des E’tudes Scientifique 34, no. 1 (1968): 105–12.

Atiyah, M. F., and G. Segal. “Equivariant K-theory and Completion.” Journal of Differential Geometry 3, no. 1–2 (1969): 1–18.

Adams, J. F. “Quillen’s Work on Formal Groups and Complex Cobordism.” In Stable Homotopy and Generalised Homology (Chicago Lectures in Mathematics). University of Chicago Press, 1995. ISBN: 9780226005249. [reprint of the 1974 original]

Quillen, D. G. “The Spectrum of an Equivariant Cohomology Ring: I.” Annals of Mathematics 94, no. 3 (1971): 549–72.

May, J. P. The Geometry of Iterated Loop Spaces (Lectures Notes in Mathematics). Vol. 271. Springer-Verlag, 1972.

Quillen, D. G. “On the Cohomology and K-theory of the General Linear Groups Over a Finite Field.” Annals of Mathematics 96, no. 3 (1972): 552–86.

———. “Algebraic K–theory I.” In Higher K-Theories (Lecture Notes in Mathematics). Vol. 341. Springer, 1973, pp. 85–147. ISBN: 9783540064343.

Nishida, G. “The Nilpotency of Elements of the Stable Homotopy Groups of Spheres.” Journal of the Mathematical Society of Japan 25, no. 4 (1973): 707–32.

Adams, J. F. Stable Homotopy and Generalised Homology (Chicago Lectures in Mathematics). University of Chicago Press, 1995. ISBN: 9780226005249. [reprint of the 1974 original]

Segal, G. “Categories and Cohomology Theories.” Topology 13, no. 3 (1974): 293–312.

Bousfield, A. K. “The Localization of Spaces with Respect to Homology.” Topology 14, no. 2 (1975): 133–50.

Griffiths, P. A., and J. W. Morgan. Rational Homotopy Theory and Differential Forms. Birkh ̈auser, 1981. ISBN: 9783764330415.

Adams, J. F. “Prerequisites (on equivariant stable homotopy theory) for Carlsson’s lecture.” In Algebraic Topology (Lecture Notes in Mathematics). Vol. 1051. Springer-Verlag, 1984, pp. 483–532. ISBN: 9780387129020.

Waldhausen, F. “Algebraic K-theory of Spaces.” In Algebraic and Geometric Topology (Lecture Notes in Mathematics). Vol. 1126. Springer, 1985, pp. 318–419. ISBN: 9783540152354.

Most of the papers read in the seminar are available online, through the MIT library’s VERA database. You need an MIT certificate to use it. Many journals are also available directly through MathSciNet.

For mainly German documents visit Goettinger Digitalisierungs-Zentrum and follow links to Mathematical Literature.

For much earlier work, try la bibliotheque Gallica-Math. The most useful link from there is to NUMDAM, an archive of seminars and other mathematical documents. I especially commend to you the Seminaire Henri Cartan:

Year 1950–51: Cohomologie des groupes, suite spectrale, faisceaux

Years 1953–55: Algebre d’Eilenberg-Maclane et homotopie

Year 1958–59: Invariant de Hopf et operations cohomologiques secondaires

Year 1959–60: Periodicite des groupes d’homotopie stable des groupes classiques, d’apres Bott

For more recent work, the standard preprint server is the Front for the Mathematics ArXiv.

Course Info

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Fall 2014
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