nLab Anderson duality




The stable (infinity,1)-category of spectra has a dualizing object (dualizing module) on a suitable subcategory of finite spectra. It is called the Anderson spectrum I I_{\mathbb{Z}} (Lurie, Example 4.3.9). The duality that this induces is called Anderson duality.


The Anderson dual of the sphere spectrum is discussed in

The Anderson dual of KU is (complex conjugation-equivariantly) the 4-fold suspension spectrum Σ 4KU\Sigma^4 KU (Heard-Stojanoska 14, theorem 8.2). This implies that, nonequivariantly KUKU is Anderson self-dual and the Anderson dual of KOKO is Σ 4KO\Sigma^4KO, which were both first proven by Anderson.

Similarly Tmf[1/2][1/2] is Anderson dual to its 21-fold suspension (Stojanoska 12).



Original articles include

  • Donald W. Anderson, Universal coefficient theorems for K-theory, mimeographed notes, Univ. California, Berkeley, Calif., 1969 (pdf)

  • Zen-ichi Yosimura, Universal coefficient sequences for cohomology theories of CW-spectra, Osaka J. Math. 12 (1975), no. 2, 305–323. MR 52 #9212

See also


The Anderson dual of the sphere spectrum is discussed (in a context of extended TQFTs) in

The Anderson duals of KU and of tmf are discussed in

Equivariant duality

Anderson duality in equivariant stable homotopy theory is discussed in

Last revised on September 9, 2021 at 17:17:22. See the history of this page for a list of all contributions to it.