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Coeur de l'invariant de Casson et cobordismes d'homologie

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(1)Coeur de l’invariant de Casson et cobordismes d’homologie Kristell Dequidt Picot. To cite this version: Kristell Dequidt Picot. Coeur de l’invariant de Casson et cobordismes d’homologie. Mathématiques [math]. Université de Nantes, 2005. Français. �tel-00009786�. HAL Id: tel-00009786 https://tel.archives-ouvertes.fr/tel-00009786 Submitted on 20 Jul 2005. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(43) , G7L A ˆpt~R8xÓÏ n AGAA(AA(A(AA(AAGAA(A(AA(AA(AGAA(AA(AA(A(AA G =>= 7L A G A G  6#75w}~$w‚5 A(AA(A(AA(AAGAA(A(AA(AA(AGAA(AA(AA(A(AA G =>= 7L A G A <  y|{‚vxÓ{‚†8‡t{}w‚vxw}~R89†V„8 n tbÓÏV„89†v9ÓÏ$ b89†Vt[y|Ï$~$w‚vxÓ{}w xÏR89† G = G L7A G A H „8 ˆpé´89tvx~R~R8x8xÓÓÏ ÏR† 8x~yvx~$w‚5÷„89†~ 7w‚†$~R†„8 8xÛ5a†$ÓÏ{‚89†vŽÛ[y|ˆpt7† G = AA(A(AA(AAGAA(A(AA(AA(AGAA(AA(AA(A(AA L <  | y ‚ { x v  Ó * {  8 ‡   t } { ‚ w x v } w R ~ ( 8  „ 8 tUÓÏVÓ5tÏR

(44) „‡Ów}~„8~ 7w‚†R~R†V„8( 8xÛ5 AA G =IJ 7L A k < 0 Ñ R Ï x 8  Ó ´ é ( 8 ‡ „ ¬ Ó $ ~ 7 Û 9 6   " Ï xˆ;8 7L A < A G AXA(A(AA(AA(AGAA(AA(AA(A(AA G = P G 7L A A < < 8xˆ²y|Ï"&uÓ78†$ÓÏ{‚8(†ŽÓ7†?݃>ÏRÓtb8 GIG = HL7A 7L A y|{‚A vxÓ{*8‡t{}w‚vxw}~R8(„8 d tUÓÏVÓ5tÏR

(45) „‡ÓVw}~„8A~ 7A(w‚AG†R~RA†VA(„8(A A(8xAÛA(5 A(AAAA GIGIG 7L A H A G 57†$~$Ï$Ó7vx~$w‚5/„ , Ó578 b5578 L Ýé>y|Ï$w‚6x~R6 W A(AA(AA(A(AA GIG H 7L A H A < Ñ^8x~$w}~R8¬„‡w}ƒ>ÏR89†R†$w‚5 : # ‡57†²Ó578~$Ï$w}é

(46) wzy|{}w‚†Žy|~$w‚5v9ˆpt{‚88 „8 TH AåAA(AA(A(AA(AAGAA(A(AA(AA(AGAA(AA(AA(A(AA GIG ? 7L A H A H Ñ0ÏR8xÓé´8(„‡Ó¬~$Û769Ï"xˆ;8 7L A H A G A(A(AA(AA(AGAA(AA(AA(A(AA GIG P g. g,1. g,1. g,1. X. X. X γ. X γ. X. g,1. X. γ. γ. J. g,1.

(47) ­. ¨壁¥D¢¡W#¢  ¥[¢ RC R  R¦Ý¥[¢  ¥ ¥  ¥7ŸG¥£ &Ÿ ¡¢ ¥]*¢  h#€¦W €¡Ý¥. z¡€£>¥7Ÿu¢¤¥DR

(48) £>¡# FV. RC $  F ;\79358?/0>D3 ]793d;\)^46-07 7; ]>F] b]T-07  7 < 7 D79) >da#) ]> >&) /08?17T8  #>d1 >d-A> D/07 'CE , ? A G  ‡w‚†$~R8x57v98„ , Ó5pvRÛ[y|ˆpt;„8é´89vx~R8xÓÏR† ¤~R8xˆpt7† X†RÓÏ*Ó5pv9 UÏR„‡w‚†$ˆ;8 „ , Û7ˆ;{‚ƒ>w‚8 AAGAA(AA(A(AA(AAGAA(A(AA(AA(AGAA(AA(AA(A(AA G >H = ? A <  UÏR„‡w‚†$ˆ;89†€„ , Û7ˆ;{‚ƒ>w‚8 SU Ýt[y|ώy|{}{‚6x{}w‚†Žy|~$w‚57†*8x~€8‡~R8x57†$w‚5Gv98x5$ ~$ώy|{‚8 A(AA(A(AAGAA(AA(A(AA(AAGAA(A(AA(AA(AGAA(AA(AA(A(AA G H L ? A < A G  6#75w}~$w‚5©„ , Ó578 H Ýé>y|Ï$w‚6x~R6J†Êy|57† UÏR„/y†Ž†Ruvxw‚698 ;Ó5Üv9  UÏR„‡w‚†$ˆ;8„ , Û7ˆ;{‚ƒ>w‚8 AGAA(A(AA(AA(AGAA(AA(AA(A(AA G H L ? A < A < SU Ýt[y|ώy|{}{‚6x{}w‚†Êy|~$w‚57† ÏR8x{zy|~$w}é´89†8x~ v9 UÏR„‡w‚†$ˆ;89† „ , Û7ˆ;{‚ƒ>w‚8 G >H ? ? A < A H  ‡~R8x57†$w‚5¬v98x5u~$ώy|{‚8(tUÓÏ{‚8ƒ>ÏRÓtb8 A(AAGAA(A(AA G LIL ? A H  ‡~R8x57†$w‚5¬„‡Ó¬v9

(49) vxè‡vx{‚8„8(.38xè´8xÏy|Ó$÷v9 UÏR„‡H(Σ) w‚†$ˆ;89†„ , Û7ˆ;{‚ƒ>w‚8 G L J  ";\) a#]I;?a5)^7T8  a -A79)=)^79-04C;?/A@D798 7; 7 F;\79358?/0>D3 a ]T>F] b]T-07* /23d;\79) 8?7T]I;?/0>D3 '  J A G  6#75w}~$w‚53„89†V†R~$Ï$Ó7vx~$ÓÏR89†„ ,-0Ó{‚8xÏÏR8x{zy|~$w}é´89†8x~tÏRtÏ$w‚6x~R69† A(A(AA G ? L J A < +ÏRÓtU8y†R†R

(50) vxw‚6 y|Ó$v9 bÏR„‡w‚†$ˆ;89†*„ , Û7ˆ;{‚ƒ>w‚8 ˆJÓ5w‚†€„ , Ó578 †$~$Ï$Ó7v ~$ÓÏR89†„ ,- Ó{‚8xÏÏR8x{zy|~$w}é´89† G ?>? J A H Û7ˆ;ˆ;Ï$tÛw‚†$ˆ;8XvxÏRw‚†R68xA(~A8‡A(~R8xA57AG†$w‚A5¬A(„‡A(ÓAv9A(

(51) vxAè

(52) A(vx{‚AG8GA„ , A(w}5•A~R8xA(ÏR†RA89vxA(~$w‚A(5 AAA G >J < J A L Ñ^8xÏR†$tb89vx~$w}é´89† AAGAA(AA(A(AA(AAGAA(A(AA(AA(AGAA(AA(AA(A(AA G >J ? . . .

(53) . . . . . . . P. .

(54)

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(56)  x0 89†$~Ó5 tbw}5u~J„‡Ó¯ UÏR„ €y|w}57†$w &uÓ78;†$ÓÏ(†Êy†R6xÏ$w‚8 pv98x$5  F := π1 (Σg,1 , x0 ) ~$ώy|{‚8„89†Rv98x57„7y|5•~R8y†R†R

(57) vxw‚698 {F } A %5²57~R8Vy|{‚ÏR† M (k) {‚8†RÓ7?† ݃>ÏRÓtU8„8 &•Ów0y|ƒ>w}~~$Ï$w}é

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(59) vxw‚8p6xƒ•y|{‚8xˆ;8x5•C ~  k Û7ˆ;ˆ;Ï$tÛw‚†Rˆ;8G„D 8 ´Û57†Ž5 7„5•~{‚M 8 57g,1 ¹è•(k) y|Ó389†R~ M (k + 1) A  t[y|Ï$~$w}Ï÷„‡Ó„8x$Ó ‡w xˆ;83Û7ˆ;ˆ;Ï$tÛw‚†$ˆ;8܄ 8 ´Ûg,157†R5 τ „6 #75w †$ÓÏ K  ./Ï$w}~Žyav957†$~$Ï$Ów}~Ó5/Û7ˆ;ˆ;Ï$tÛw‚†$ˆ;8 q : K → Q A &8G„6ÈÒÝ2y|Ó~ 8x5•~$ÏR8 q 8x~ g,1λ∗ 89†R~Ó5Û7ˆ;ˆ;Ï$tÛw‚†$ˆ;8 d : K → Z &•Ów é´6xg,1 Ï$-w #[8 g,1. λ∗ =. 1 d + q. 24. .3Ï$w}~ŽyGv95Þ189vx~$ÓÏR8 8 &•Ó78V~RÓ~R8 H P†$tÛ xÏR8„ , Û7ˆ;{‚ƒ>w‚8 8x5•~$w xÏR8tb8xÓ~ /x~$ÏR8 ~R8  5uÓ78t[y|Ï0Ó5;†Rvxw}57„8xˆ;8x5u~„8"898xƒ•y>y|ÏR„;†$ÓÏåÓ5²6x{‚6xˆ;8x5•~„‡Óp~$ÏRw‚†$w xˆ;8V†RÓ7†?݃>ÏRÓtU8 „7y|57†{zy #7{}~$ώy|~$w‚5¯„8 ´5Û75 M (3) bƒ´6x576xώy|{‚8xˆ;8x5•~G57~R6 L ]tUÓÏÓ5©v98x?Ï  ~Žy|w}5 g A Ñ^y|Ïv957†$~$Ï$Ó7vx~$w‚5  q †¹,šy|5g,15uÓ{‚83†RÓÏ!v983†RÓ7?† ݃>ÏRÓtU8 A g,189†$~$ÏR8xw}5•~  L  g,1.  Σ      "!#$%$&')(

(60) $* $&+ ,-./0&1&32.4&3465  3$+')(7+8 29782;: <=?>@> .&AB21*C

(61)  /0D(7+8 F := F  F = [F, F ] (7   k ≥ 1 : g,1. 1. k+1. M. k.

(62) {Ý, Û7ˆ;ˆ;Ï$tÛw‚†Rˆ;8 d „8n.3Ï$w}~Žy!89†$~„57vXtÏRtbÏ$~$w‚5578x{ 5¬y|ttU8x{}{‚8xώy d {‚8 |v ÓÏ÷„8{Ý, w}5uéy|Ï$wzy|5u~„8J y†R†Ž5 A. λ∗ A. ,-89†$~ tbÓÏ"&uÓ7w.  , Û7ˆ;ˆ;Ï$tÛw‚†$ˆ;8 89†$~a„6#75wv9ˆpˆ;8 |„‡w-, 6xÏR8x57v98 8x5u~$ÏR83<©v9

(63) vxè‡vx{‚89†¯: {‚8nv9

(64) vxè

(65) vx{‚8p„8n./8xè´8xÏ &•Ódw089†$~ Ó5¯v9

(66) vxè

(67) vx{‚8n„8p†$w}ƒ>5[y|~$ÓÏR8 8x~Ó5©v9

(68) vxè

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(70)  

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(142) ÎXÆ }Æxá;ÌxÍ[Î ϕ Ë•Ì M }Ì σ ÉúÍ[ç¤×ÅÈɑׁÍ]ÎGËÚ RفÚNØ ‚Ì T , m (T )  ϕ X ϕ çÆÈÅÊÉ ÌGÍ]×>ΑÚ

(143) ÅRÌ  ‚ÌÈá²ÌÈÍ[Î  Æ ´×  ÉâÎPÆ(ÇÊÚ

(144) Éâg,1 ç¤×Í[ÎP

(145) Ì XÌ Ø Ú•Ç 7؇Ù>ÚuÅ g ≥ 3  d ÌÊÇÈÎ Ú

(146) Í7ÉxÚÌ $RÙ  

(147) ×âÍbÌ çÆÈÅÊÉ ׁÍ]Î Æ ´×  ÉâÎPÆØ]Å$ÆŽÆ$˕ÌÈÍ]ÎPÌ  X Ó7†tUÓ鴁57†y|{‚ÏR†v¹y|{‚vxÓ{‚8xÏ d tbÓÏ{‚8v¹y†?Pvx{‚6(„ , Ó5~ 7w‚†$~„8 8xÛ5 : #+9>&)917 

(148) 

(149) 

(150)  É τγ ÌÊÇÈÎ ‚Ì!Î0XÉzÇxÎ˕ÌXÌ •Í ÜˁÅ$فɑÎPÌ}Ì}فÍÜË•Ì γ

(151) ¹ÌÈÅÊá²ÆRÌ Ø  فÍ •ÆRÌn˴ׁÍ7Ç Σ ×  Ù>ÅŽÇ g,1 Ù   = ±1.  X dX (τγ ) = (nX γ − 1)(nγ + 1) 8xˆ²y|"Ï &uÓ757† &uÓ&,-8x5²ÏR8xé´8x5[y|5•6~  {zy(„6 #75w}~$w‚5!„8 8x~„89†v9uvxè‡vx{‚89† 8x~  v98~$Û769"Ï xˆ;8tU8xÏ$ˆ;8x~V„8 v¹y|{‚vxÓ{‚8xÏ d tbÓÏ Ó5tÏR

(152) „‡Ódw}X~„8 ~ 7w‚†$~R†V„8  8xÛcX5„57τv ~$Û769Ï$w &uÓ78xˆ;8x5•~tUÓÏ~RÓ~„‡-w ,U69ˆ;XÏ$tÛw‚†Rˆ;8G„8 M A g,1  y|57†G{zy #75 „‡Ó vŽÛ[y|tw}~$ÏRc 8 H$ 57Ó7†Gw}ÏR57†(Ó5¯tU8xÓ©t{}Ó7†({‚w}5 &uÓ78p„7y|57 † -./ G  A 57†Rw‚„6xÏR57†{‚8†RÓ7?† ݃>ÏRÓtU8 „8 ҔÏ$ˆ;6t[y|Ï{‚89† „‡-w ,U69ˆ;Ï$tÛw‚†Rˆ;89B† &•Ów y|ƒ>w‚†Ž†R8x5•~0~$Ï$w}é

(153) wzy|{‚8xˆ;8x5•~†$ÓÏå{‚89† VvRÛ[g,1y|ˆpt7†M„8g,1é´89vx~R8xÓÏR†575;†$w}5ƒ>Ó{}w‚8xÏR† †$ÓÏ0{zy†$ÓÏ1ÒÝyv98 A {‚ÏR†^{Ý,šy|tt{}w‚v¹y|~$w‚5 d ÏR89†$~$ÏR8xw}5u~R8  V 89†$~^Ó5JÛ7ˆ;ˆ;Ï$tÛw‚†Rˆ;8 A 8t{}Ó7† ¤57Ó7† g,1 y¹é´57†V{‚8 ~$Û769"Ï xˆ;8J†$ÓXw}éy|5u~G: #+9>&)917

(154) 

(155) 0f

(156)  É ϕ ÌÈÇÈÎ]ÚuÍ²Æ ‚ÆÈá²ÌÈÍ[Î Ë•Ì Vg,1 × }فÅÊ0Ç }Ì σ ÉúÍ7ç|ׁÅÊɔׁÍ[Î σ Tϕ, mX (Tϕ) ÍUÌG˕ÆØÌÈÍ]ËG؇ׁÇJËÚ  

(157) Ù>É à÷ËÚ  ‡×áØ ËuÌ(ç2Ì 9ÎPÌÈÚ

(158) ŎÇXÍ]فÍ3ÇÊÉâÍ Ú ¶ÉÝÌÈÅ X ÇÊÚ

(159) Å Σ  g,1 Ñ^y|Ïv957†R6 &uÓ78x5•~ ]{zy SU Ýt[y|ώy|{}{‚6x{}w‚†Žy|~$w‚5©„8J./Ï$w}~Žya„89†ˆ²y|ttw}5ƒ÷~RÏR8ny†R†R  vxw‚69†Vy|$Ó ÷6x{‚6xˆ;8x5•~R†„8 V 578 „6xtU8x57„÷t[y†„‡ÓvRÛ[y|ˆpt¬„8é´89vx~R8xÓÏR† X v957†Rw‚„6xÏR6  5 {zy÷57~R8xώy¬y|{‚ÏR† m(Tg,1) tbÓÏ ϕ ∈ V A  8²t{}Ó7† &8x{}{‚8²89†R~(5[y|~$ÓÏR8x{}{‚8xˆ;8x5•~n{‚8 v9ˆpt{‚8 ‡-w #[6„ , Ó578 SOÝt[ϕy|ώy|{}{‚6x{}w‚†Êy|~$w‚5 &•g,1 Ó9w ‡8x{}{‚8 „6xtU8x57„!„‡ÓvŽÛ[y|ˆpt¬„8é´89vx~R8xÓÏR† Ó7†y9鴁57†y|{‚ÏR†V{‚8(v9ÏR{}{zy|w}ÏR8(†$Ów}é>y|5•~G: XA Z*>D),>d-2-A46/0)^7

(160) 

(161) 

(162)  فÚu!Ç ‚ÌÊÇ dX RÙ úÍ 9ɑ˕ÌxÍ[Î ÇÊÚ

(163) Å Vg,1 ˕Æ  Í7ÉúǎÇ9ׁÍ[ΠׁÉâÍÇÊÉÚuÍ 

(164) Ù  á;فá;فÅPØ •ÉúÇÊá²Ì d˜ : V → Z ˕Æ  Í[Éb؇ׁ Å cX = 3τ + δdX .. . g,1. d˜ : Vg,1 → Z. . ϕ 7→ σ Tϕ , m(Tϕ ) .. GH.

(165) v957†$~$w}~$Ó78Ó5¬†RÓ7† ݃>ÏRÓtb8(„8 V A Z*>D),>d-2-A46/0)^7

(166) 

(167) ,

(168) ÄׁŠRفÍÇxΑÅÊÚ 9ΑɔفÍ   

(169) فá;فá;فÅPØ g,1•ÉúÇÊá²Ì d˜ Ø]Å1Ù فÍ•Ì  

(170) Ù>ápÙ  á;فÅPØ •ÉúÇÊá²Ì d ˕ÌÜفÅÊɑÎÝ×  €yÜ~$ÏRw‚†$w xˆ;8¬t[y|Ï$~$w‚8„8v98ˆ²y|5uÓ7†RvxÏ$w}~²tUÏ$~R8†$ÓÏ;{Ý,-8 ‡~R8x57†$w‚5„89†av9uvxè‡vx{‚89† „8./8xè´8xÏ8x~„ , w}5•~R8xÏR†R89vx~$w‚5¬y|$Ó ²v9 UÏR„‡w‚†$ˆ;89† „ , Û7ˆ;{‚ƒ>w‚8 A y|57†{‚8vRÛ[y|tw}~$ÏR8$?  57Ó7†å„6 #75w}ÏR57†0Ó578 8 ‡~R8x57†$w‚5pv98x5•~$ώy|{‚8 tUÓÏ*{‚8ƒ>ÏRÓtU8 H y†R†R

(171) vxw‚6y|$Ó Jv9 U?Ï  „‡w‚†Rˆ;89†G„ , Û7ˆ;{‚ƒ>w‚8!†$ÓÏ Σ A Ñ^ÓÏXv98x{z$y €v957†$w‚„6xÏR57†GÓ5g,1vRÛ[y|ˆpt „8pé´89vx~R8xÓÏR† 575©†$w}5ƒ>Ó{}w‚8xÏ X †RÓÏ Σ y|g,1w}57†Rw &uÓ78J{zy²~$Ï$w}é

(172) wzy|{}w‚†Žy|~$w‚5¯„8 I × Σ v957†R~Žy|5•~R8n{‚8 {‚5ƒJ„8 I w}57„‡Ów}~R8t[y|Ï {zy g,1„‡w}ÏR89vx~$w‚5atÏR6Èґ6xÏR698„8 I 8x~ X A uw (M, i±g,1) 89†$~0Ó5²v9 U?Ï  „‡w‚†Rˆ;8„ , Û7ˆ;{‚ƒ>w‚8 7y|{‚ÏR† 8x{}{‚8w}57„‡Ów}~Ó578†R89vx~$w‚5 X „‡Ó SO(3) #7 ÏR6 P(TM ) y|$Ó P„89†Ž†$Ó7† „8 ∂M éuwzyG{‚8„‡-w , 69ˆ;Ï$tÛw‚†$ˆ;8 Φ &•Ówbw‚M„8x5•~$-w #[8{‚8 bÏR„!„8 M y¹é´89v M {‚8 UÏR„„8 I × Σ Ô‘vÈÒ #7ƒa<´Õ A g,1 &8ƒ>ÏRÓtU8. Kg,1. X. X. (i+ )∗ X.    . ΦM. (i− )∗ X Σ−. I × Σg,1 . b<. †R89vx~$w‚5. XM. M. †$ÓÏ{‚8 bÏR„¬„8. 

(173)   Σ+. MA. %5 tU8xÓ~Xy|{‚ÏR†Xv957†$w‚„6xÏR8xÏG{Ý,-8x57†R8xˆJ {‚8 P (M, X) „89† SU Ýt[y|ώy|{}{‚6x{}w‚†Žy|~$w‚57† ÏR8x{zy|~$w}é´89†ny|Ó v9ˆpt{‚8 

(174) -w #[6!„8 X A ,-89su†$~GÓ5 89†$t[yv98÷y;578ay|Ó$P„89†R†$Ó7†X„8 M %5¯„6 #75w}ώy!Ó578nM w Þ$89vx~$w‚5©tÏR6Èґ6xÏR698X8x5u~$ÏR8 P (M, X) 8x~ H 3 (M ∂M ; Z) ' Z A su 7y|ttU8x{‚698 σÝw}5•é>y|Ï$wzy|5•~ÏR8x{zy|~$w Ò : Z „8. σr : Psu (M, X) → Z.. € yÏR8x{zy|~$w‚5;„8 bÏR„‡w‚†$ˆ;8 „ , Û7ˆ;{‚ƒ>w‚8tÏR69†Ž8xÏ$é´8{‚8 σÝw}5•é>y|Ï$wzy|5•~ÏR8x{zy|~$w Ò A w}57†$w9 5tU8xÓ~„6#75w}ÏV{Ý,-8x57†Ž8xˆG {‚8 Hb X : ) + 3 /A;?/0>D3 

(175) & 

(176) 2'

(177)  ,-8x57†R8xˆGg,1 {‚8 Hbg,1X 89†R~ {Ý,-8x57†R8xˆG {‚8„89†v9Ót{‚89† (M, αM ) ´

(178) 89†$~*Ó5Xv9 UÏR„‡w‚†$ˆ;8„ , Û7ˆ;{‚ƒ>w‚8 †$ÓÏ 8x~å

(179) y|tt[y|Ï$~$w‚8x5•~  P (M, X)  M su ˆJÓ5w€„8{zyXÏR8x{zy|~$w‚5/„ ,-6 &•Ów}é>y|{‚8x57v98(„6 #75Σw‚g,1 8(t[y|Ï(: αM ( 8x~ †R5u~V UÏR„7y|5•~R† 8x~ σM(M,Nα ) = σ (N, α ) (M, αM ) ∼ (N, αN ) <=> r. M. r. N. € yJ{‚wbtÏR

(180) „‡Ów}~†$ÓÏ H w}57„‡Ów}~5[y|~$ÓÏR8x{}{‚8xˆ;8x5•~VÓ578{‚w „8ƒ>ÏRÓtb8 †$ÓÏ y|Ó7†Ž†$w&5 ~$w‚8x5•~Ó578(8

(181) ~Rg,1 8x57†Rw‚5¬v98x5•~$ώy|{‚8a: 0. /Z. bX /H. / Hg,1. /1. bX H g,1. (∗)..   $& >  (     8'& *+   $& 2& * ++ /@1*1&  9782  897 $ * 8!

(182) ( 8    I × D (   /0 &  $& >0>  >  978 2 ,+(7  ) "  > 8  / > /0" >  σ) 0/  +8/@  : . 2. g,1. GL. :. M.

(183) uw 89†$~ Ó5÷y|Ó~$ÏR8vŽÛ[y|ˆpt!„8é´89vx~R8xÓÏR†575!†$w}5ƒ>Ó{}w‚8xÏ †$ÓÏ 

(184) y|{‚ÏR†{Ý,-8‡~R8x5$ R† w‚5¬v98xY5•~$ώy|{‚8Xy†R†R

(185) vxw‚698 Hb Y 89†$~6&uÓw}é>y|{‚8x5•~R8  (∗) A  8t{}Ó7†ΣÏR89g,1†$~$ÏR8xw}5•~R8  M  g,1 {Ý,-8‡~R8x57†$w‚5¬v98x5u~$ώy|{‚8 (∗) 89g,1†$~V6&uÓw}éy|{‚8x5u~R8  (?) A. &8 σÝ w}5•é>y|Ï$wzy|5•~ÏR8x{zy|~$w Ò # 8 Ó578(Ï$w}ƒ>w}578tÏR6ÈҔ6xÏR698;: ) + 3 /A;?/0>D3

(186) 

(187) 2'&'

(188) Ñ^ÓÏ~RÓ~ v9 bÏR„‡w‚†Rˆ;8G„ , Û7ˆ;{‚ƒ>w‚8 (M, i±) †$ÓÏ Σg,1 {zy  }ØׁÅ1×  ‚Æ  ÉzÇ9×>ΑɑÙ>Í'ÅRÌ }×>ΑÉâç|ÌÜË  Î‘É ´×  89†$~;{Ý, Ó5w &uÓ78¬6x{‚6xˆ;8x5u~a„8 Psu(M, X) „8 Ýw}5uéy|Ï$wzy|5u~ÏR8x{zy|~$w Ò05•Ó{ A σ 8x~$~R8(v957†$~$Ï$Ó7vx~$w‚53„6 #75w}~Ó578(†R89vx~$w‚5 sb „8 (∗) : 0 #+9>&)917

(189) 

(190) 2'CE

(191) Ä×>Å RفÍÇxΑÅÊÚ 9ΑɔفÍ   ×Ç9Ì 9ΑɑÙ>Í sb0 Ø]Å1Ù  فÍ •Ì  ×ǹ2Ì 9ΑɔفÍ;Ë  Î‘É ´× ËuÌ (?)   ÙÍ ŽÙ   ‚Ì 0 ×|ǎÇ9Ù xÉÝÆaÌÊÇxÎVÚ

(192) Í ŽÙ   ‚Ì÷˕ÌnÇÈÉ >Í]×>ΑÚ

(193) Å$Ì xÚ

(194) É^Ø]Å1Ù  فÍ •Ì 3τ Ù  τ ÌÈÇÈÎ }Ì RÙ   ‚ÌpË•Ì cbÜ Ì ´ÌxÅ  &8² Ó~X„‡Ó vŽÛ[y|tw}~$ÏR8 J¬89†$~J„8²tÏR{‚5ƒ´8xÏn{‚8²v9

(195) vxè

(196) vx{‚8a„ , w}5•~R8xÏR†R89vx~$w‚5 y|$Ó  v9  UÏR„‡w‚†$ˆ;89†„ , Û7ˆ;{‚ƒ>w‚8 8x5 †$Ów}é>y|5•~{zy †$~$ώy|~R6xƒ>w‚8 „8©.3Ï$w}~Žy tUÓÏ„6 #75w}ÏÓ5 Û7ˆ;ˆ;Ï$tÛw‚†Rˆ;8vxÏRw‚†R6 A y|57†n{zy/v957†$~$Ï$Ó7vx~$w‚5„8÷.3Ï$w}~Žy/tUÓÏn{‚89†nˆ²y|ttw}5ƒ vxè

(197) {}w}57„‡ÏR89† 5Ó~$w}{}w‚†R8¬{zy©„‡w}ÏR89vx~$w‚5tÏR6ÈҔ6xÏR698¬„8 v9ˆpˆ;8¬tÏR8xˆpw‚8xÏaé´89vx~R8xÓÏ!„‡Ó vŽÛ[y|ˆpt©„8GÏR8x=t xÏR89† A &8X Ó~6x~Žy|5u~ „8X„6 #75w}Ï Ó5/I„8x$Ó ‡w xˆ;8nvRÛ[y|ˆpt¯„8Jé´89vx~R8xÓÏR†  w}57„6xtU8x57„7y|5•~„‡ÓatÏR8xˆpw‚8xÏ 

(198) 8x5aÓ~$w}{}w‚†Žy|5•~{‚8„6ÈҔy|Ó~„ , Û7ˆ;~Rtw‚88x5u~$ÏR8 X 8x~ ϕ X A ∗ Ó7†^„6 #75w}ÏR57†å{zy57~$w‚5p„8vŽÛ[y|ˆptp„8é´89vx~R8xÓÏR†^~R8xˆpt7†å†$Óπ{‚89†^v9 UÏR„‡w‚†$ˆ; 89† „ , Û7ˆ;{‚ƒ>w‚8a: ) + 3 /A;?/0>D3

(199) 

(200) 2' 

(201) 5 vRÛ[y|ˆpt „8pé´89vx~R8xÓÏR†(~R8xˆpt7†J†$ÓÏ 89†$~Ó5 vRÛ[y|ˆpt „8 é´89vx~R8xÓÏR†575†$w}5ƒ>Ó{}w‚8xφ$ÓÏ M &•Ów&v9Ï$ÏR89†Rtb57„ X{zyn„‡w}ÏR89vx~$w‚M 53tÏR6Èґ6xÏR698(„8 I †$ÓÏ é

(202) wzy Φ A ∂M M #+9>&)917 

(203) & 

(204) 2'9e

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