Goodwillie Tower and the EHP Sequence.
- 1st ed.
- 1 online resource (109 pages)
- Memoirs of the American Mathematical Society ; v.218 .
- Memoirs of the American Mathematical Society .
Intro -- 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.