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 $L{Spin}$.References
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Additional Information
- Gerd Laures
- Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, NA1/66, D-44780 Bochum, Germany
- MR Author ID: 641823
- Received by editor(s): March 26, 2014
- Received by editor(s) in revised form: August 20, 2014, September 5, 2014, September 23, 2014, and September 30, 2014
- Published electronically: November 6, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 7339-7357
- MSC (2010): Primary 55N34, 55R40; Secondary 55P50, 22E66
- DOI: https://doi.org/10.1090/tran/6575
- MathSciNet review: 3471093