LEADER 04187nam 2200613 450 001 9910480981103321 005 20170822144443.0 010 $a0-8218-9014-X 035 $a(CKB)3360000000464086 035 $a(EBL)3114507 035 $a(SSID)ssj0000888965 035 $a(PQKBManifestationID)11523062 035 $a(PQKBTitleCode)TC0000888965 035 $a(PQKBWorkID)10866572 035 $a(PQKB)10277464 035 $a(MiAaPQ)EBC3114507 035 $a(PPN)195419154 035 $a(EXLCZ)993360000000464086 100 $a20150416h20112011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 14$aThe Goodwillie tower and the EHP sequence /$fMark Behrens 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2011. 210 4$dİ2011 215 $a1 online resource (90 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 218, Number 1026 300 $a"July 2012, Volume 218, Number 1026 (fourth of 5 numbers)." 311 $a0-8218-6902-7 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""A.4. Geometric boundary theorem""""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 218, Number 1026. 606 $aHomotopy groups 606 $aAlgebraic topology 606 $aSpectral sequences (Mathematics) 608 $aElectronic books. 615 0$aHomotopy groups. 615 0$aAlgebraic topology. 615 0$aSpectral sequences (Mathematics) 676 $a514/.24 700 $aBehrens$b Mark$f1975-$0902308 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480981103321 996 $aThe Goodwillie tower and the EHP sequence$92016954 997 $aUNINA