Duals of higher real K-theories at p = 2
Abstract
We study $\mathrm{K}(h)$-local Spanier-Whitehead duality for $C_{2^n}$-equivariant Lubin-Tate spectra, $E_h$, at the prime $2$ and heights $h$ divisible by $2^{n-1}$. We determine a $C_{2^n}$-equivariant equivalence $DE_h\simeqΣ^{-V_h} E_h$, for an explicit $C_{2^n}$-representation, $V_h$. We then study the $\mathrm{RO}(C_{2^n})$-periodicities of $E_h$ at some low heights. With these ingredients, we determine the self-duality of some higher real $K$-theories up to a specified suspension shift, at some low-heights. In particular, we show that $DE_4^{hC_8}\simeq Σ^{112}E_4^{hC_8}$.
Fields of Study & Subjects
Black Holes and Theoretical Physics
Advanced Topology and Set Theory
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 495
- Pages
- 110974–110974
- Publication date
- 20 April 2026
- Language
- EN