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 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 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 of modular forms for congruence subgroup
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, -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.