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Transactions of the American Mathematical Society

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Characteristic classes in $ TMF$ of level $ \Gamma_1(3)$


Author: Gerd Laures
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
Published electronically: November 6, 2015
MathSciNet review: 3471093
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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{\mathit String}$ and $ B{\mathit 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{\mathit Spin}$.


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Additional Information

Gerd Laures
Affiliation: Fakultät für Mathematik, Ruhr-Universität Bochum, NA1/66, D-44780 Bochum, Germany

DOI: https://doi.org/10.1090/tran/6575
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
Article copyright: © Copyright 2015 American Mathematical Society