group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
spin geometry, string geometry, fivebrane geometry …
rotation groups in low dimensions:
see also
The Ochanine genus lifts to a homomorphism of ring spectra $M Spin \to KO[ [q] ]$ from spin structure cobordism cohomology theory to Tate K-theory (Kreck-Stolz 93, lemma 5.8, lemma 5.4).
Moreover, localized at 2 this map factors (Kreck-Stolz 93, last line of p. 18 and cor 5.2 and page 21) through a map
where $el$ is a 2-local spectrum (at least closely related to tmf0(2)) whose coefficient ring is the coefficient ring for the Ochanine elliptic genus
wich, after inversion of 2, surjects onto the ring $\mathbb{Z}[\tfrac{1}{2}][\delta, \epsilon]$ of modular forms for congruence subgroup $\Gamma_0(2)$
This is Kreck-Stolz 93, theorem 1 (while we follow in notation Hovey 95, page 2), which is a kind of refinement of the SO orientation of elliptic cohomology due to (Landweber-Ravenel-Stong 93).
If this map of ring spectra could be shown to be “highly structured” in that it preserves E-∞ ring structure, then it would equivalently be a universal orientation (see at relation between orientations and genera).
(Hovey 95), for the moment see at cobordism theory determining homology theory
partition functions in quantum field theory as indices/genera/orientations in generalized cohomology theory:
Matthias Kreck, Stefan Stolz, $HP^2$-bundles and elliptic homology, Acta Math, 171 (1993) 231-261 (pdf)
Mark Hovey, Spin Bordism and Elliptic Homology, Mathematische Zeitschrift 219, 163-170 1995 (web)
Peter Landweber, Douglas Ravenel, Robert Stong, Periodic cohomology theories defined by elliptic curves, in Haynes Miller et. al. (eds.), The Cech centennial: A conference on homotopy theory, June 1993, AMS (1995) (pdf)
Last revised on November 4, 2020 at 11:46:05. See the history of this page for a list of all contributions to it.