nLab
Anderson duality

Contents

Idea

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.

Examples

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).

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

References

General

Original articles include

  • D. W. Anderson, Universal coefficient theorems for K-theory, mimeographed notes, Univ. California, Berkeley, Calif., 1969.

  • 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

Examples

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 October 31, 2017 at 00:31:12. See the history of this page for a list of all contributions to it.