The Goodwillie tower and the EHP sequence / / Mark Behrens

• Record Nr.: UNINA9910480981103321
• Autore: Behrens Mark <1975->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2011; ©2011
• ISBN: 0-8218-9014-X
• Descrizione fisica: 1 online resource (90 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 218, Number 1026
• Disciplina: 514/.24
• Soggetti: Homotopy groups; Algebraic topology; Spectral sequences (Mathematics); Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "July 2012, Volume 218, Number 1026 (fourth of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Abstract""; ""Introduction""; ""0.1. Conventions""; ""Chapter 1. Dyer-Lashof operations and the identity functor""; ""1.1. The operadic bar construction""; ""1.2. The cooperadic structure on B()""; ""1.3. Operad structure on *(Id)""; ""1.4. Homology of extended powers""; ""1.5. Dyer-Lashof-like operations""; ""Chapter 2. The Goodwillie tower of the EHP sequence""; ""2.1. Fiber sequences associated to the EHP sequence""; ""2.2. Homological behavior of the fiber sequences""; ""2.3. Transfinite Atiyah-Hirzebruch spectral sequences""; ""2.4. Transfinite Goodwillie spectral sequence""""Chapter 3. Goodwillie filtration and the P map""; ""3.1. Goodwillie filtration""; ""3.2. The genealogy of unstable elements""; ""3.3. Behavior of the E and P maps in the TAHSS""; ""3.4. Behavior of the E and P maps in the TGSS""; ""3.5. Detection in the TGSS""; ""3.6. Relationship with Whitehead products""; ""Chapter 4. Goodwillie differentials and Hopf invariants""; ""4.1. Hopf invariants and the transfinite EHPSS""; ""4.2. Stable Hopf invariants and metastable homotopy""; ""4.3. Goodwillie d1 differentials and stable Hopf invariants""; ""4.4. Higher Goodwillie differentials and unstable Hopf invariants""""; 4.5. Propagating differentials with the P and E maps""; ""4.6. Calculus form of the Whitehead conjecture""; ""4.7. Exotic Goodwillie differentials""; ""Chapter 5. EHPSS differentials""; ""5.1. EHPSS naming conventions""; ""5.2. Using the TGSS to compute the H map""; ""5.3. TEHPSS differentials from TGSS differentials""; ""5.4. A bad differential""; ""Chapter 6. Calculations in the 2-primary Toda range""; ""6.1. AHSS calculations""; ""6.2. Calculation of the GSS for S1""; ""6.3. GSS calculations""; ""6.4. Calculation of the EHPSS""""6.5. Tables of computations""; ""6.5.1. The AHSS for k(L(1))""; ""6.5.2. The AHSS for k(L(2))""; ""6.5.3. The AHSS for k(L(3))""; ""6.5.4. The EHPSS""; ""6.5.5. The GSS for n+1(S1)""; ""6.5.6. The GSS for n+2(S2)""; ""6.5.7. The GSS for n+3(S3)""; ""6.5.8. The GSS for n+4(S4)""; ""6.5.9. The GSS for n+5(S5)""; ""6.5.10. The GSS for n+6(S6)""; ""Appendix A. Transfinite spectral sequences associated to towers""; ""A.1. The Grothendieck group of ordinals""; ""A.2. Towers""; ""A.3. The transfinite homotopy spectral sequence of a tower""; ""A.4. Geometric boundary theorem""""Bibliography""