Computational methods for higher real K-theory with applications to tmf
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2006
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/34545 |
| _version_ | 1826216922683801600 |
|---|---|
| author | Hill, Michael Anthony, Ph. D. Massachusetts Institute of Technology |
| author2 | Michael J. Hopkins. |
| author_facet | Michael J. Hopkins. Hill, Michael Anthony, Ph. D. Massachusetts Institute of Technology |
| author_sort | Hill, Michael Anthony, Ph. D. Massachusetts Institute of Technology |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. |
| first_indexed | 2024-09-23T16:55:35Z |
| format | Thesis |
| id | mit-1721.1/34545 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:55:35Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/345452019-04-12T09:19:02Z Computational methods for higher real K-theory with applications to tmf Hill, Michael Anthony, Ph. D. Massachusetts Institute of Technology Michael J. Hopkins. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. Includes bibliographical references (p. 67-69). We begin by present a new Hopf algebra which can be used to compute the tmf homology of a space or spectrum at the prime 3. Generalizing work of Mahowald and Davis, we use this Hopf algebra to compute the tmf homology of the classifying space of the symmetric group on three elements. We also discuss the E3 Tate spectrum of tmf at the prime 3. We then build on work of Hopkins and his collaborators, first computing the Adams-Novikov zero line of the homotopy of the spectrum eo4 at 5 and then generalizing the Hopf algebra for tmf to a family of Hopf algebras, one for each spectrum eop_l at p. Using these, and using a K(p - 1)-local version, we further generalize the Davis-Mahowald result, computing the eop_1 homology of the cofiber of the transfer map [...]. We conclude by computing the initial computations needed to understand the homotopy groups of the Hopkins-Miller real K-theory spectra for heights large than p- 1 at p. The basic computations are supplemented with conjectures as to the collapse of the spectral sequences used herein to compute the homotopy. by Michael Anthony Hill. Ph.D. 2006-11-07T12:53:16Z 2006-11-07T12:53:16Z 2006 2006 Thesis http://hdl.handle.net/1721.1/34545 71011916 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 69 p. 3600879 bytes 3603677 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Hill, Michael Anthony, Ph. D. Massachusetts Institute of Technology Computational methods for higher real K-theory with applications to tmf |
| title | Computational methods for higher real K-theory with applications to tmf |
| title_full | Computational methods for higher real K-theory with applications to tmf |
| title_fullStr | Computational methods for higher real K-theory with applications to tmf |
| title_full_unstemmed | Computational methods for higher real K-theory with applications to tmf |
| title_short | Computational methods for higher real K-theory with applications to tmf |
| title_sort | computational methods for higher real k theory with applications to tmf |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/34545 |
| work_keys_str_mv | AT hillmichaelanthonyphdmassachusettsinstituteoftechnology computationalmethodsforhigherrealktheorywithapplicationstotmf |