Characteristics for \(\mathcal{E}_\infty\) ring spectra. (English) Zbl 1475.55013
Ausoni, Christian (ed.) et al., An alpine bouquet of algebraic topology. Alpine algebraic and applied topology conference, Saas-Almagell, Switzerland, August 15–21, 2016. Proceedings. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 708, 1-17 (2018).
Summary: We introduce a notion of characteristic for connective \(p\)-local \(\mathcal E_\infty\) ring spectra and study some basic properties. Apart from examples already pointed out by M. Szymik [Algebr. Geom. Topol. 14, No. 6, 3717–3743 (2014; Zbl 1311.55014)], we investigate some examples built from Hopf invariant \(1\) elements in the stable homotopy groups of spheres and make a series of conjectures about spectra for which they may be characteristics; these appear to involve hard questions in stable homotopy theory.
For the entire collection see [Zbl 1392.55001].
For the entire collection see [Zbl 1392.55001].
MSC:
| 55P43 | Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.) |
| 55P42 | Stable homotopy theory, spectra |
| 55P48 | Loop space machines and operads in algebraic topology |
Keywords:
stable homotopy theory; \(\mathcal{E}_\infty\) ring spectrum; commutative \(S\)-algebra; cell algebra; power operationsCitations:
Zbl 1311.55014References:
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