$TMF_0(3)$ Characteristic classes for String bundles

preprint2015arXivOpen access

We compute the completed $TMF_0(3)$ cohomology of the 7-connective cover $BString$ of $BO$ . We use cubical structures on line bundles over elliptic curves to construct an explicit class which together with the Pontryagin classes freely generates the cohomology ring.

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$TMF_0(3)$ Characteristic classes for String bundles

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TMF0(3)TMF_0(3)TMF0​(3) Characteristic classes for String bundles

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$TMF_0(3)$ Characteristic classes for String bundles