Inverting the Hopf map
We calculate the η-localization of the motivic stable homotopy ring over C, confirming a conjecture of Guillou and Isaksen. Our approach is via the motivic Adams-Novikov spectral sequence. In fact, work of Hu, Kriz and Ormsby implies that it suffices to compute the corresponding localization of the...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
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Oxford University Press (OUP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/116020 https://orcid.org/0000-0001-8702-1127 |
| _version_ | 1811094324321976320 |
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| author | Andrews, Michael Joseph Miller, Haynes R |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Andrews, Michael Joseph Miller, Haynes R |
| author_sort | Andrews, Michael Joseph |
| collection | MIT |
| description | We calculate the η-localization of the motivic stable homotopy ring over C, confirming a conjecture of Guillou and Isaksen. Our approach is via the motivic Adams-Novikov spectral sequence. In fact, work of Hu, Kriz and Ormsby implies that it suffices to compute the corresponding localization of the classical Adams-Novikov E₂-term, and this is what we do. Guillou and Isaksen also propose a pattern of differentials in the localized motivic classical Adams spectral sequence, which we verify using a method first explored by Novikov. |
| first_indexed | 2024-09-23T15:58:14Z |
| format | Article |
| id | mit-1721.1/116020 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T15:58:14Z |
| publishDate | 2018 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1160202022-09-29T17:22:55Z Inverting the Hopf map Andrews, Michael Joseph Miller, Haynes R Massachusetts Institute of Technology. Department of Mathematics Andrews, Michael Joseph Miller, Haynes R We calculate the η-localization of the motivic stable homotopy ring over C, confirming a conjecture of Guillou and Isaksen. Our approach is via the motivic Adams-Novikov spectral sequence. In fact, work of Hu, Kriz and Ormsby implies that it suffices to compute the corresponding localization of the classical Adams-Novikov E₂-term, and this is what we do. Guillou and Isaksen also propose a pattern of differentials in the localized motivic classical Adams spectral sequence, which we verify using a method first explored by Novikov. 2018-05-31T14:20:55Z 2018-05-31T14:20:55Z 2017-11 2018-05-25T19:12:39Z Article http://purl.org/eprint/type/JournalArticle 1753-8416 1753-8424 http://hdl.handle.net/1721.1/116020 Andrews, Michael and Haynes Miller. “Inverting the Hopf Map.” Journal of Topology 10, 4 (November 2017): 1145–1168 © 2017 London Mathematical Society https://orcid.org/0000-0001-8702-1127 http://dx.doi.org/10.1112/topo.12034 Journal of Topology Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Andrews, Michael Joseph Miller, Haynes R Inverting the Hopf map |
| title | Inverting the Hopf map |
| title_full | Inverting the Hopf map |
| title_fullStr | Inverting the Hopf map |
| title_full_unstemmed | Inverting the Hopf map |
| title_short | Inverting the Hopf map |
| title_sort | inverting the hopf map |
| url | http://hdl.handle.net/1721.1/116020 https://orcid.org/0000-0001-8702-1127 |
| work_keys_str_mv | AT andrewsmichaeljoseph invertingthehopfmap AT millerhaynesr invertingthehopfmap |