The Goodwillie Tower and the EHP Sequence is popular PDF and ePub book, written by Mark Behrens in 2012, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Goodwillie Tower and the EHP Sequence can be Read Online from any device for your convenience.
The Goodwillie Tower and the EHP Sequence Book PDF Summary
The author studies the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime $2$. Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. He relates the Goodwillie filtration to the $P$ map, and the Goodwillie differentials to the $H$ map. Furthermore, he studies an iterated Atiyah-Hirzebruch spectral sequence approach to the homotopy of the layers of the Goodwillie tower of the identity on spheres. He shows that differentials in these spectral sequences give rise to differentials in the EHP spectral sequence. He uses his theory to recompute the $2$-primary unstable stems through the Toda range (up to the $19$-stem). He also studies the homological behavior of the interaction between the EHP sequence and the Goodwillie tower of the identity. This homological analysis involves the introduction of Dyer-Lashof-like operations associated to M. Ching's operad structure on the derivatives of the identity. These operations act on the mod $2$ stable homology of the Goodwillie layers of any functor from spaces to spaces.
Detail Book of The Goodwillie Tower and the EHP Sequence PDF
- Author : Mark Behrens
- Release : 20 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821869024
- Genre : Mathematics
- Total Page : 109 pages
- Language : English
- PDF File Size : 7,6 Mb
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