The Goodwillie tower and the EHP sequence
 Responsibility
 Mark Behrens.
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xi, 90 p. : ill ; 26 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1026.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA3 .A57 NO.1026  Unknown 
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Creators/Contributors
 Author/Creator
 Behrens, Mark, 1975
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 DyerLashof operations and the identity functor
 The Goodwillie tower of the EHP sequence
 Goodwillie filtration and the P map
 Goodwillie differentials and Hopf invariants
 EHPSS differentials
 Calculations iin the 2primary Toda range.
 Publisher's 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 AtiyahHirzebruch 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 DyerLashoflike 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.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2012
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1026
 Note
 "July 2012, volume 218, number 1024 (fourth of 5 numbers)."
 ISBN
 9780821869024 (pbk. : alk. paper)
 0821869027 (pbk. : alk. paper)