In and Around Stable Homotopy Groups of Spheres /
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Author / Creator: | Xu, Zhouli, author. |
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Imprint: | 2017. Ann Arbor : ProQuest Dissertations & Theses, 2017 |
Description: | 1 electronic resource (299 pages) |
Language: | English |
Format: | E-Resource Dissertations |
Local Note: | School code: 0330 |
URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11715033 |
Other authors / contributors: | University of Chicago. degree granting institution. |
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ISBN: | 9780355077650 |
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. English |
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. |
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