Characteristic classes in 𝑇𝑀𝐹 of level Γ₁(3)

Laures, Gerd

doi:10.1090/tran/6575

Characteristic classes in $TMF$ of level $\Gamma _1(3)$
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Abstract:

Let $TMF_1(n)$ be the spectrum of topological modular forms equipped with a $\Gamma _1(n)$-structure. We compute the $K(2)$-local $TMF_1(3)$-cohomology of $B{String}$ and $B{Spin}$: both are power series rings freely generated by classes that we explicitly construct and which generalize the classical Pontryagin classes. As a first application of this computation, we show how to construct $TMF(3n)$-cohomology classes from stable positive energy representations of the loop groups $L{Spin}$.

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