nLab
tmf0(2)

Context

Elliptic cohomology

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

Where tmf is obtained from the moduli stack of elliptic curves, tmf 0(2)tmf_0(2) (or its versions Tmf 0(2)Tmf_0(2), TMF 0(2)TMF_0(2)) denotes the spectrum obtained from the cover by the moduli stack of elliptic curves with level structure for the congruence subgroup Γ 0(2)\Gamma_0(2) (the one that preserves the NS-R spin structure on an elliptic curve, see here).

Detailed discussion is in (Behrens 05).

This plays at least roughly the role for the Ochanine elliptic genus (the partition function of the type II superstring in the NS-R sector) as tmf does for the Witten genus (the partition function of the heterotic superstring). See at spin orientation of Ochanine elliptic cohomology for more.

Properties

Relation to Landweber-Ravenel-Stong-Ochanine elliptic spectrum

After inversion of 6, TMF 0(2)TMF_0(2) is (Behrens 05) the elliptic spectrum EllEll of (Landweber-Ravenel-Stong 93).

Periodicity

The periodicity of TMF 0(2)TMF_0(2) is 8.

References

Revised on May 13, 2014 09:38:35 by Urs Schreiber (88.128.80.82)