Topological modular forms with level structure: decompositions and duality

preprint2022arXivOpen access

Abstract

Topological modular forms with level structure were introduced in full generality by Hill and Lawson. We show that these decompose additively in many cases into a few simple pieces and give an application to equivariant TMFTMF. Furthermore, we show which Tmf1(n)Tmf_1(n) are self-Anderson dual up to a shift, both with and without their natural C2C_2-action.

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