Bar constructions for topological operads and the Goodwillie derivatives of the identity
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
| मुख्य लेखक: | |
|---|---|
| अन्य लेखक: | |
| स्वरूप: | थीसिस |
| भाषा: | en_US |
| प्रकाशित: |
Massachusetts Institute of Technology
2005
|
| विषय: | |
| ऑनलाइन पहुंच: | http://hdl.handle.net/1721.1/27881 |
| _version_ | 1826212157888397312 |
|---|---|
| author | Ching, Michael (Michael Comyn) |
| author2 | Haynes Miller. |
| author_facet | Haynes Miller. Ching, Michael (Michael Comyn) |
| author_sort | Ching, Michael (Michael Comyn) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005. |
| first_indexed | 2024-09-23T15:17:16Z |
| format | Thesis |
| id | mit-1721.1/27881 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:17:16Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/278812019-04-10T18:19:43Z Bar constructions for topological operads and the Goodwillie derivatives of the identity Ching, Michael (Michael Comyn) Haynes Miller. 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, 2005. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 105-106). We describe a cooperad structure on the simplicial bar construction on a reduced operad of based spaces or spectra and, dually, an operad structure on the cobar construction on a cooperad. Further, we show that if the homology of the original operad (respectively, cooperad) is Koszul, then the homology of the bar (respectively, cobar) construction is the Koszul dual. We use our results to construct an operad structure on the partition poset models for the Goodwillie derivatives of the identity functor on based spaces and show that this induces the 'lie' operad structure on the homology groups of these derivatives. Finally, we extend the bar construction to modules over operads (and, dually, to comodules over cooperads) and show that based spaces naturally give rise to modules over the operad formed by the derivatives of the identity. by Michael Ching. Ph.D. 2005-09-26T15:58:42Z 2005-09-26T15:58:42Z 2005 2005 Thesis http://hdl.handle.net/1721.1/27881 61212201 en_US 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 106 p. 566833 bytes 564666 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Ching, Michael (Michael Comyn) Bar constructions for topological operads and the Goodwillie derivatives of the identity |
| title | Bar constructions for topological operads and the Goodwillie derivatives of the identity |
| title_full | Bar constructions for topological operads and the Goodwillie derivatives of the identity |
| title_fullStr | Bar constructions for topological operads and the Goodwillie derivatives of the identity |
| title_full_unstemmed | Bar constructions for topological operads and the Goodwillie derivatives of the identity |
| title_short | Bar constructions for topological operads and the Goodwillie derivatives of the identity |
| title_sort | bar constructions for topological operads and the goodwillie derivatives of the identity |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/27881 |
| work_keys_str_mv | AT chingmichaelmichaelcomyn barconstructionsfortopologicaloperadsandthegoodwilliederivativesoftheidentity |