Abstract
We bound the volume of the homotopy groups of the 2-local Goodwillie approximations of a sphere in terms of the amount of 2-torsion in the stable stems, providing a Goodwillie-theoretic refinement of a result of Burklund and Senger. At the (Formula presented.) -excisive approximation, this bound is obtained by ‘multiplying the stable answer by a polynomial of degree (Formula presented.) ’. The main tool is Behrens' Goodwillie–EHP long exact sequence.
| Original language | English |
|---|---|
| Pages (from-to) | 1530-1539 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 55 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Jun 2023 |
| Externally published | Yes |
Funding
I would like to thank Niall Taggart for his encouragement and helpful comments, and for making me aware of the paper [ 1 ] of Arone and Kankaanrinta. I would also like to thank Stephen Theriault and Charlotte Summers for their help and advice, and acknowledge the technical debt to Burklund and Senger. I am grateful to the anonymous referee for the suggestion that the results of the first version of this paper could be substantially improved. This paper was written while the author was a postdoc at the University of Southampton, funded by an EPSRC Doctoral Prize (Grant number EP/T517859/1).
| Funders | Funder number |
|---|---|
| Engineering and Physical Sciences Research Council | EP/T517859/1 |
| University of Southampton |
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