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

In the context of heterotic string theory:

Equivariant duality

Anderson duality in equivariant stable homotopy theory is discussed in

Last revised on September 8, 2023 at 10:38:01. See the history of this page for a list of all contributions to it.