The Goodwillie tower for S[superscript 1] and Kuhn's Theorem
We analyze the homological behavior of the attaching maps in the 2–local Goodwillie tower of the identity evaluated at S¹. We show that they exhibit the same homological behavior as the James–Hopf maps used by N Kuhn to prove the 2–primary Whitehead conjecture. We use this to prove a calculus for...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Mathematical Sciences Publishers
2012
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| Online Access: | http://hdl.handle.net/1721.1/70018 |
| _version_ | 1811070385316167680 |
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| author | Behrens, Mark Joseph |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Behrens, Mark Joseph |
| author_sort | Behrens, Mark Joseph |
| collection | MIT |
| description | We analyze the homological behavior of the attaching maps in the 2–local Goodwillie tower of
the identity evaluated at S¹. We show that they exhibit the same homological behavior
as the James–Hopf maps used by N Kuhn to prove the 2–primary Whitehead conjecture. We use this to prove a calculus form of the Whitehead conjecture: the Whitehead sequence is a contracting homotopy for the Goodwillie tower of S¹ at the prime 2. |
| first_indexed | 2024-09-23T08:35:08Z |
| format | Article |
| id | mit-1721.1/70018 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:35:08Z |
| publishDate | 2012 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | mit-1721.1/700182022-09-23T13:03:31Z The Goodwillie tower for S[superscript 1] and Kuhn's Theorem The Goodwillie tower for S¹ and Kuhn's Theorem Behrens, Mark Joseph Massachusetts Institute of Technology. Department of Mathematics Behrens, Mark Joseph Behrens, Mark Joseph We analyze the homological behavior of the attaching maps in the 2–local Goodwillie tower of the identity evaluated at S¹. We show that they exhibit the same homological behavior as the James–Hopf maps used by N Kuhn to prove the 2–primary Whitehead conjecture. We use this to prove a calculus form of the Whitehead conjecture: the Whitehead sequence is a contracting homotopy for the Goodwillie tower of S¹ at the prime 2. 2012-04-13T16:18:49Z 2012-04-13T16:18:49Z 2011-09 2011-08 Article http://purl.org/eprint/type/JournalArticle 1472-2747 1472-2739 http://hdl.handle.net/1721.1/70018 Behrens, Mark. “The Goodwillie Tower for S¹ and Kuhn’s Theorem.” Algebraic & Geometric Topology 11.4 (2011): 2453–2475. Web. en_US http://dx.doi.org/10.2140/agt.2011.11.2453 Algebraic & Geometric Topology Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Mathematical Sciences Publishers MIT web domain |
| spellingShingle | Behrens, Mark Joseph The Goodwillie tower for S[superscript 1] and Kuhn's Theorem |
| title | The Goodwillie tower for S[superscript 1] and Kuhn's Theorem |
| title_full | The Goodwillie tower for S[superscript 1] and Kuhn's Theorem |
| title_fullStr | The Goodwillie tower for S[superscript 1] and Kuhn's Theorem |
| title_full_unstemmed | The Goodwillie tower for S[superscript 1] and Kuhn's Theorem |
| title_short | The Goodwillie tower for S[superscript 1] and Kuhn's Theorem |
| title_sort | goodwillie tower for s superscript 1 and kuhn s theorem |
| url | http://hdl.handle.net/1721.1/70018 |
| work_keys_str_mv | AT behrensmarkjoseph thegoodwillietowerforssuperscript1andkuhnstheorem AT behrensmarkjoseph thegoodwillietowerfors1andkuhnstheorem AT behrensmarkjoseph goodwillietowerforssuperscript1andkuhnstheorem |