group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
Write $\mathbb{S}$ for the sphere spectrum and tmf for the connective spectrum of topological modular forms.
Since tmf is an E-∞ring spectrum, there is an essentially unique homomorphism of E-∞ring spectra
Regarded as a morphism of generalized homology-theories, this is called the Hurewicz homomorphism, or rather the Boardman homomorphism for $tmf$
(Boardman homomorphism in $tmf$ is 6-connected)
The Boardman homomorphism in tmf
induces an isomorphism on stable homotopy groups (hence from the stable homotopy groups of spheres to the stable homotopy groups of tmf), up to degree 6:
(Hopkins 02, Prop. 4.6, DFHH 14, Ch. 13)
Michael Hopkins, section 4 of Algebraic topology and modular forms, Proceedings of the ICM, Beijing 2002, vol. 1, 283–309 (arXiv:math/0212397)
Christopher Douglas, John Francis, André Henriques, Michael Hill, Chapter 13 of: Topological Modular Forms, Mathematical Surveys and Monographs Volume 201, AMS 2014 (ISBN:978-1-4704-1884-7)
Last revised on September 7, 2020 at 15:57:55. See the history of this page for a list of all contributions to it.