Topics seminar in algebraic topology

In the spring 2011, we ran a short seminar on the telescope conjecture, a major problem in chromatic homotopy theory.

Time: (some) Tuesdays 2-3 PM, unless otherwise noted.
Location: 241 Altgeld.

Date Speaker Title Notes
March 15, 11 AM Martin Frankland Finite localizations and the telescope conjecture Main reference: [6]
April 5 Martin Frankland Equivalent statements of the conjecture Notes from the talk
April 12 Nat Stapleton The thick subcategory theorem  
April 19, 11 AM Charles Rezk The Adams-Novikov spectral sequence of the telescope  
April 26 Bertrand Guillou Construction of type n complexes  
May 3 Charles Rezk The solution for n=1  

Useful references

  1. M. Hopkins and J. Smith, Nilpotence and stable homotopy theory II. Ann. of Math. (2) 148 (1998), no. 1, 1-49.
  2. M. Hovey, Bousfield localization functors and Hopkins' chromatic splitting conjecture. The Cech centennial (Boston, MA, 1993), 225-250, Contemp. Math., 181, AMS, Providence, RI, 1995.
  3. M. Hovey, vn-elements in ring spectra and applications to bordism theory. Duke Math. J. 88 (1997), no. 2, 327-356.
  4. M. Hovey, N. Strickland, Morava K-theories and localisation. Mem. Amer. Math. Soc. 139 (1999), no. 666.
  5. M. Mahowald, D. Ravenel, and P. Shick, The triple loop space approach to the telescope conjecture. Homotopy methods in algebraic topology (Boulder, CO, 1999), 217-284, Contemp. Math., 271, AMS, Providence, RI, 2001.
  6. H. Miller, Finite localizations. Papers in honor of José Adem. Bol. Soc. Mat. Mexicana (2) 37 (1992), no. 1-2, 383-389.
  7. D. Ravenel, Localization with respect to certain periodic homology theories. Amer. J. Math. 106 (1984), no. 2, 351-414.
  8. D. Ravenel, Life after the telescope conjecture. Algebraic K-theory and algebraic topology (Lake Louise, AB, 1991), 205-222, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 407, Kluwer Acad. Publ., Dordrecht, 1993.
  9. D. Ravenel, Nilpotence and periodicity in stable homotopy theory, Ann. of Math. Stud., 128, Princeton Univ. Press, Princeton, NJ, 1992.

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