Theorem A establishes 125 nonzero v_2^32-periodic families in the 2-primary stable stems, 50 new, all vanishing in TMF yet detected by the Atkin-Lehner fixed point spectrum J_0(3).
The descent spectral sequence for topological modular forms
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abstract
We prove the Gap Theorem for the spectrum of topological modular forms $\mathrm{Tmf}$. This removes a longstanding circularity in the literature, thereby confirming the computation of $\pi_\ast \mathrm{tmf}$ from over two decades ago by Hopkins and Mahowald. Our approach is crucially a modern one, developing and refining many techniques in synthetic spectra.
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On periodic families in the stable stems of height two
Theorem A establishes 125 nonzero v_2^32-periodic families in the 2-primary stable stems, 50 new, all vanishing in TMF yet detected by the Atkin-Lehner fixed point spectrum J_0(3).