Homotopy Theory Topics Seminar

Fall 2013

Topic: Localizations and completions in topology.
Time: Wednesdays 2:30 - 3:30 PM, unless otherwise noted.
Location: MC 108.

Date Speaker Title References
September 18 Daniel Schäppi Overview and motivation
September 25 Marcy Robertson Localization of spaces A.K. Bousfield. The localization of spaces with respect to homology. Topology 14, 133-150, 1975.
October 2 Marcy Robertson Localization of spaces, part 2  
October 9 Mike Misamore Localization of spectra A.K. Bousfield. The localization of spectra with respect to homology. Topology 18, no. 4, 257-281, 1979.
October 16 No meeting today. Happy Thanksgiving.    
October 23 Martin Frankland The R-nilpotent completion A.K. Bousfield and D.M. Kan. Homotopy limits, completions and localizations. Lecture Notes in Mathematics, Vol. 304. Springer-Verlag, 1972. (Chapters 1-2)
October 30 Martin Frankland Relation between completion and localization
November 6 Omar Ortiz Rational homotopy theory via commutative dg algebras
  • K. Hess. Rational homotopy theory: a brief introduction. Interactions between homotopy theory and algebra, 175-202, Contemp. Math., 436, AMS, 2007.
  • D. Sullivan. Infinitesimal computations in topology. Inst. Hautes √Čtudes Sci. Publ. Math. No. 47, 269-331, 1978. (Sections 1-8)
  • Y. Félix, S. Halperin, J.-C. Thomas. Rational Homotopy Theory. Graduate Texts in Mathematics, 205. Springer-Verlag, 2001. (Chapters 10-12)
November 13 Enxin Wu Rational homotopy theory via dg Lie algebras
November 20 Hugo Bacard p-adic homotopy theory M. Mandell. $E_{\infty}$ algebras and p-adic homotopy theory. Topology 40, no. 1, 43-94, 2001.
November 27 Mike Misamore Morava K-theories and the chromatic tower
  • D. Ravenel. Nilpotence and periodicity in stable homotopy theory. Annals of Mathematics Studies, 128. Princeton University Press, 1992. (Sections 1.5 and 7.5)
  • J. Lurie. Chromatic Homotopy Theory. Lectures 22-24 and 32.
December 4 Daniel Schäppi The thick subcategory theorem

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