In and Around Stable Homotopy Groups of Spheres /

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Bibliographic Details
Author / Creator:Xu, Zhouli, author.
Ann Arbor : ProQuest Dissertations & Theses, 2017
Description:1 electronic resource (299 pages)
Format: E-Resource Dissertations
Local Note:School code: 0330
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Other authors / contributors:University of Chicago. degree granting institution.
Notes:Advisors: Peter May; Dan Isaksen Committee members: Mark Behrens; Paul Goerss; Dan Isaksen; Peter May.
Dissertation Abstracts International, Volume: 78-12(E), Section: B.
Summary:My thesis focuses on computations of stable homotopy groups of spheres, with applications and connections to differential geometry and motivic homotopy theory. The Adams spec- tral sequences and Toda brackets play a major role in my work. We have introduced two methods to compute Adams differentials and solve extension problems: one is very technical but inductive, using the algebraic Kahn-Priddy theorem; the other one is more systematic, using a new connection between motivic homotopy theory and chromatic homotopy theory. Combining both methods, we have computed stable stems into a larger range. As a consequence, I solved the strong Kervaire invariant problem in dimension 62 and showed that the 61-sphere has a unique smooth structure, which is the last odd dimensional case.