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The descent spectral sequence for topological modular forms
Christian Carrick, Jack Morgan Davies, Sven van Nigtevecht
We prove the Gap Theorem for the spectrum of topological modular forms . This removes a longstanding circularity in the literature, thereby confirming the computation…
On periodic families in the stable stems of height two
Christian Carrick, Jack Morgan Davies
We discover a host of infinite periodic families in the 2-primary stable homotopy groups of spheres. We also confirm the existence of many families predicted by Hopkins--Mahowald.…
Descent spectral sequences through synthetic spectra
Christian Carrick, Jack Morgan Davies, Sven van Nigtevecht
The synthetic analogue functor from spectra to synthetic spectra does not preserve all limits. In this paper, we give a necessary and sufficient criterion for to preserve…
A synthetic approach to detecting -periodic families
Christian Carrick, Jack Morgan Davies
We provide a simple proof that the unit map from the sphere spectrum to the connective image-of- spectrum is surjective on homotopy groups. This is achieved using a…
Nonvanishing of products in -periodic families at the prime
Christian Carrick, Jack Morgan Davies
Many products amongst -periodic families in the stable homotopy groups of spheres are shown not to vanish and some Toda brackets are shown not to contain zero. This is done by…