Symmetric spectra reading seminar.
This page contains information about the symmetric spectra reading seminar. For information about other activities of the topology group at the University of Copenhagen, please visit this page.

What are symmetric spectra?
Symmetric spectra are used to construct the stable homotopy category in much the same way as the derived category of a ring is constructed from chain complexes. One main feature is that there is a commutative and associative smash product on symmetric spectra that descends to the usual smash product in the stable homotopy category. Another benefit in comparison to other approaches to stable homotopy theory is that defining symmetric spectra does not require a lot of machinery.

What are we doing?
We are reading selected parts of the book (in preparation) [S] by Stefan Schwede and the paper [HSS] by M. Hovey, B. Shipley and J. Smith, and other related papers. Participants take turns in presenting the material to each other.

Starting Jan 29, we meet on *Thursdays at 14:15 in room 04.4.01*.

Past meetings:

2008
 Sep 16  Antonio Diaz,        (Propaedeutic) Spectra and generalized cohomology theories.
 Sep 23  Tarje Bargheer,      Definitions and basic properties of symmetric spectra. [S]
 Sep 30  Alexander Berglund,  Examples: Sphere spectrum, Eilenberg-MacLane spectra. [S]
 Oct 7   Jens Kaad,           Examples: Algebraic K-theory spectrum. [S] [L]
 Oct 14  -                    - 
 Oct 21  Nathalie Wahl,       Smash product on symmetric spectra. [HSS]
 Oct 28  Antonio Diaz,        (Propaedeutic) Survey on model categories.
 Nov 4   Alexander Berglund,  Stable equivalences of symmetric spectra. [HSS]
 Nov 11  Alexander Berglund,  Stable equivalences of symmetric spectra (continued).
 Nov 18  -                    - 
 Nov 25  Tarje Bargheer,      Stable model structure on symmetric spectra. [HSS]
 Dec 2   Tarje Bargheer,      Stable model structure on symmetric spectra (continued).
 Dec 9   Otgonbayar Uuye,     Comparison between symmetric and ordinary spectra. [BF] [HSS] [S]

2009
 Jan 20  Otgonbayar Uuye,     KK-theory as a non-commutative stable homotopy theory.
 Jan 29  Antonio Diaz,        Symmetric spectra and Topological Hochschild Homology. [Sh]
 Feb 5   -                    -
 Feb 12  -                    -
 Feb 19  Ib Madsen,           From THH to TC.
 Feb 26  Alexander Berglund,  Smash product on diagram spectra. [MMSS]
 Mar 5   Alexander Berglund,  Smash product on diagram spectra (continued).
 Mar 12  -                    -
 Mar 19  Ib Madsen,           Equivariant spectra and TC.

Please go to this page.

 
   [BF]   A.K. Bousfield and E. M. Friedlander, Homotopy theory of Γ-spaces, spectra,
             and bisimplicial sets, Lecture Notes in Math. 658, 1978, pp. 80-130.
   [HSS]  M. Hovey, B. Shipley and J. Smith, Symmetric spectra,
             J. Amer. Math. Soc. 13 (2000), no. 1, 149-208.
   [L]    J-L. Loday, K-théorie algébrique et représentations de groupes,
             Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 3, 309-377.
   [MMSS] M. Mandell, J.P. May, S. Schwede, B. Shipley, Model Categories of Diagram Spectra,
             Proc. London Math. Soc. (3) 82 (2001), no. 2, 441-512.
   [S]    S. Schwede, Symmetric spectra,
             Book in preparation.
   [Sh]   B. Shipley, Symmetric Spectra and Topological Hochschild Homology,
             K-Theory 19 (2000), 155-183.