HAL Id: hal-00129570
https://hal.archives-ouvertes.fr/hal-00129570
Preprint submitted on 8 Feb 2007
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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.
A theory of cobordism for non spherical links.
Vincent Blanloeil, Françoise Michel
To cite this version:
Vincent Blanloeil, Françoise Michel. A theory of cobordism for non spherical links.. 1997. �hal- 00129570�
'(*),+.-0/213+547698 :58<;5=58 >?=@8<ACB5DFEG>?HF8<=5I<8JK8<HF>?LMDFN?=!O.I<>?HFHF8<:P>?HFQ?8SR.JK>?DFI&I<N?RTN?JU:5DFVKWPO.N?=@LUX.8YVU8SLZN?[\R.DFHFDF=58<>?JZ[]N?JKW^VN_E?8<JZLUX58 DF=`LU8<Q?8<JKV0a
6bX58<=dcfefgTO2hi8j.JKN_E?8 LMX5>?LkLlhiNmncdobpq:5DFW^8<=5VUDFN?=5>?HMOrVUDFW^j5HF8&;5Rr8<JK8<:9HFDF=5s`Vq>?JK8 I<N?RTN?JU:5>?=`LkDF[t>?=5:9N?=5HFuvDF[tLMX58<u@X5>_E?8Y>?HFQ?8<R5JK>?DFI<>?HFHFu
I<N?RrN?JK:5>?=`LwG8<DF[x8<JULq[xN?JUW^V?ayzVq>?=9>?HFQ?8<R5JK>?DFIYHFDF=5sDFVz>vVUDFW^j5HF8 ;5Rr8SJU8<:dHFDF=5s{O5N?B5JkI<JKDFLM8<JKDFN?=P[]N?JqI<N?RTN?JU:5DFVKW|>?HFHFNGhVzB5VqLMNVKLMB5:5uDFVKN?HF>?LM8S:
VKDF=.Q?B5HF>?JKDFLMDF8<VN?[*I<N?W^j.HF8S}X`uCjr8<JKVUB5JK[]>?I<8SVB5jvLUN^I<N?RrN?JK:.DFVKW9a
~ ^^v
?qMPiCqC{C{iYt.qM.q{tS7i MMqPzU2¡U*F¢Z*¡£qS¤q\7i
*z i iUt¥¦iM.iM*¡CUz¥i¤qMi.F*M{bi{iqM`§¨YY..¤z.i{.©fª`¤qbY«iCq.{M.{¬
S®
©_¯°±ªn³²´¬
Gµ¶ ct·kp.¸
®
°º¹
Sµ¶ ¸ ®
°C» ¼qiMiiCqqM½¥i{C F*¾i¿M.iM{¾.Mq¥i¤qMi
iU¡q¡t.M¥iUz©½ÀÁ|q{z*ÂÄà mnÅ
Æ
*q|iqi`qiM ib.izU¤qÇ{*C{$
®
M
µ¶ Å »
iq¿È mnÅokp
Æ
É£ i¤qqqtSÊ©ÌË q¦t.M{*Ut\Í2qC{C{S¢YMq¥qi{tÎt.qqM. {Mi.ÏiÐq¦qiM
à mnci·tm
Ñ ¸ ²
okp
S®
°zÒÃ mnci·tm
Ñ
°Óq{dqq{ {qÔiqf2ziUi^.¤zÕÎU*F¦.iMÖZ» ¡q{×qzÉUi
FMØ<ÙqÚÔØSÛÜÛiÝMÛiÞißMà{áiÝÓØ]âÜÚãt@²©Ë ziCU*Ui¡q..S¢YUz¥£qMäYii.qzUC´UiCftY*qqiM
È mnct·kp
Ñ
¸å
²Y°.°.»q.
å
²°æ
² okp
S®
°.°@Ò¨È mnci·kp
Ñ
M *qÎUMq¦iв©Ë zç±MMqi.èMéiqM<*C¤q`Í
*¤z. *qi.
.ÏêFç±ëi»ìiíiîM°.q59*qqMMq
å
²°qn*.Uz{dqi iUt¥iUiZ?Y éi²©
ç±iC{5¢k.»ïÊ©ç±MUziqiiM.Îq.5¢kÎq*¬
¯©²\ð&ñ
²
ñv¬ÓÈ mnci·kp
Ñ ò å
²Y°¹ È p
U¡zUä {C{*MiqM£×qqC*Mi|qU2½Mb.F¢YUi9i#ó
ò å
²°C»
q±óôM.¤qÕ{M{ɨõiCÎtUMõtY¤qq¤qMiq{M¥i i¤q.zZ|i
å
²°.©
ö ©Ë qiqMiM
å
²° M
l÷¡ø
ö °SÍ5{izq{n*{z©
ëi©Ë qiqz{.q{éùôiv×q {i²tð&ñ
²
ñ Mfiqi`»i.M{*q»
,÷¡ø
¯°<Í2{tqq{n*.*
C¤qqiqMiMÂtÈ mnct·kp
Ñ
q5¢Mq¥
å
²°úiú i¤qzqiSi© ûv¦z{×qqF*MiÂù¾U«Ø<ÙqÚü±ßMÝUýzÛiþ ÿÊÚ{þi
å
²°.©
S®
©ö °ç±i.¥i{z{.tUFÊ»vMUd.5 *qÔ¡ÝMßUý#M
,÷ ø ö °<Í2{tqq{n*q» i.M{{q»úCZq»
{MiC{q»
ö ÷ ø
¯°qM{qCUiziÐC¤qqiqMiM½iúÈ mnci·kp
©ýqÛ&ØM.zq{CUiÐMUz
U©M{© MMq
iq<*Ci`É qi{iiCqqMÔ*È mnciokp
°.© K7MéUFÍ2q5½*qT*»iÔt* UMq
å
» q{C¦`§YMS*
±CÎq» {iqt`*»Ði.M{* ö ÷
Í5.¤qqizUiMù iÈ mnci·kp
»úz2¢YMq¥
å
ié i¤qzqiS.¤q2
iqMiMùôM{iMM{Â qÚßÚþ*Ø þáiàÚét
å ©
S®
©Mëi°&iUM5Uz¥$籩S¢ZiM.$꯻ìiîM»¼.5 *qÂ?UMq
å
iq
å p
»iqS.in*F
qMäYii.zqU±½q½.tÎiqMiM»ÏiC#à{ÛÊÛiþqáiýYØÏU«*z{.n§MS7i¾{é {zqUz¥ »
Á¬"!$ê
® ¸
¯îk¹ È mnct·kp
!ºê
® ¸
¯îU».¤q2q¬
!$#
®&%
°Pæ å
tq'
!$#&¯
%
°Pæ
ø å p ¸
q.
ø p
M@*qMUq
p
F**zt.M{*Ut¡C`¢k.C{q©
S®
©)(i°ª`£ù YÎ ö ÷
qM{qCUtqiÐt.M{*¼.* iqMiU¨i È mnci·kp
»diz#M`+* «*q
,
¤qU*éi.-
c ù
¸0/1/
° É
/1/
Í_i.CUtq©
Ë q2 qÚ{ß)Ú{þØ3Ûiþ4 iC.{M**ù¾UqqMUMqi i.65¬7*8!9*¿¹ /1/
q{×qz{ÂiúiMU5
C{iM.¡ê ö »;:
®
îq©MíiíiêFª ö »<:
®
îM»^q©_¯íi°C¬ Un
>=
¸?
°úYM@*"!$*»zq{'5
>=
¸?
° U@*zMMqUq¥
¤qé {U¦È mnct·kp
i
=
tqBA
· ?
°.»qq{CCA
· ?
°bMÓqénY{M
?
õiq¤qCq{qõÔU
È mnci·kp
ò
ù°b|*q
i.F*F¢kɨiCU*{¢k`*tf×qUÂqiCiz*ÎùôMÈ mnct·kp
©
ûvÂq×qqF*Mi£D qÚ{ß)Ú{þØÛiþ4EÛiþ9áÝMßMýF
å
MqHGz{M{SiC i.CZU{*IGqUS.¤qCi{
i
å ©
À q{
÷$J
ö »ïÊ©^ª`¢YMq
êɪd¯»ìLKiîU° tq¡ç©<S¢ZiM.
êM ö »N:
®
îU° ¥i5¢q{tÎzUn*2qi.t`*SÍ
)O{UiÂi{i iCqUC {MiC.{fiz*M{.bikÀ ÉC.Í2
,
¤qÉ¢ZiM{z{{Mi.C{tPGqUSiCÎC©
S®
©)i°QR.ß)4«ÜÝUÚ|ÝMßUýF¼Ué¦UMqÂzU2³qi
l÷¨ø
¯T°SÍ2iqq`{SGq{M{<|.¤z.i{©T UMq
å
Mϼ.MqU7×q {C{MUqºUúq{C¦`§YU<*|½qMäY.*UtqU¦×zq.Ut8U ¬È mnci·kp
ò å ¹ È p
»IU
{Mq¥*.F¢YUt^iÂó
ò å
»q{Có UõiCiUMõi {*¤qz¤qUt q{M¥iYt¤q.qÂt
å
»iq|q5¢YUq¥
,÷ ø
¯°SÍ5{izq{n*{#×qY.C»*zizq{C{q£izU2¼t.VGq{M{<Ï.¤z.i{ét
å
© ?Â*zUqi {
q{×zqUXWi¯
C{
¯©ö °.°t±
,
¤qF¢ZiUq{C{M*Mi¦i±M*¥i.ivqMUMq{ti.9qU27Mé¤z2
i.CiqqMSU*Î*zi¡õTÀ ÉC.Í2
,
¤qÉ¢ZiM{z{{õiq*qúq{iC{
ö
tq|ëi»S*¡M@Wi¯»UqFY¬
Y %&Z\[^]_a`
÷8J
ëbIcedgfBhjilkCm3n>oqpsrjotuojvnilw7xhzy0tuo|{jf&rjf0tuv&y0w.c}i~`By0w.vf0w.n'i~`Bc>o'y0o
y&nortuy0i {jy&nln'{jf&rjf0t0v&y0w.cN.oi~`0otc`0f0tkh
S®
©Mìi°û¼q×qqF*Mi¦iáiÝMÞiÚ\þ.áißMàÝMßUý¦M£MUq
å
²°fi.CZUT*{z»Piq.{CU {7i 5¢k»Y*Ï
qiMiiCqqM¥i{C ²¡F*7i¦M.iM{7.Mq¥i¤qMiCÉ?i©&¤q<*q.i.»Pç±MUqt.èMÐ*qiS#i9.Mq¥i¤qMi
{tÎzUn§³*Y {C.¤qCi{UqMM{ *qiM¥iq.iMUMqi..MqM×q {C{¨UMq.©Gq*qi. ö è
iqÂëS*¡M@Wi¯MqÉY¬
Y %&ZR]_a`
÷$J
ëbqc>dgf+y&nortuy0i {Qnilw7xhy0tuoQ{jf&rjf0tuv&y0w.cNi~`y0w.v+f0w.ni~`c>oH.oi~`0otc`0f0tkh
y0hjhf{i y&cojv+c1f|c>oilt'i nw.f0tFhpsrjothy0tuoy&nortuy0i {jy&nln'{jf&rjf0tuv&y0w.c1
?7êFª}»: ö îU»«©MË © ªb.q5{éqÓ?i i.qt*iM¥i{z.iMMUzdi^qMiqb{¤zS¢k
M©U©vq
÷ æ ¯°iCÏUC*izU©$ ?Äê«ûvÍ5ç±»sKtëiîU»qY© q¤ûúiMiqS@©úç±M2q i¤qq
¤z.Mq¥|qÏ{MiC.M{i
{tYiCqM.ã*z{i<³i«q*id籩S¢ZiM.iq¨ïÊ©Pª`¢YUz{°.»diiM
÷J
ëi»dn§YiqUéiÓqi
M.iqMbz¤\b{i iCqibiM¥i{qCiMbqT*.©Ðûú¤\bM¥iq{CiqiM¥iq.iM MUqÓi. zb.qz{.M{tkUMq.©
Gq*z{iC{ û¥iF¢k{bÎ{i i.zUC*qiS¦i iM¥i{qCiMMMq.©
&¤qSq{CÎt.{»kz2¢YMq¥iM¥i{qCiM{iMÉ£{i iCqiqGqUSiCPU@tUC««q{{.CiSÏ{iqzÉUii
{tYiCqM. iCUqMÓ×qY.éMUqkq{
÷
Ud¯@i ö ©GqP9i *iMMW0i»Éqi¤\diÎC{S.M`Ui
iqUq.Miq»³õ&2§Í5ç±UMqiCõ.{MUi
C{ÁêYÍ5ç±»«ìiìiîM°|i*qXfUn§tqq{¡YtÉYqiMiM¡i
{tYiCqi.MqU×q {C{ÂUMq9zU2¡UqMU.¬
S®
©):i°bvv oc
å
y0w.v å p
rjoc>dgfzy&nortuy0i {Qnilw7xhDy0ilw7tuoh¡m;oj{ceilonV¢
y0w.vI¢
p
y0h|{y0tuy&{cotilhcei {qm;f&nw.f0ki y&nhBf `Dkf0w.fv0tuf0kFQ_a` y0w.v
p
y0tuoB{jf&rjf0tuv&y0w.c£ceow¤ceoqmtufv0¥;{c
¢
§¦
¢ p
ilhVyIh¨¥;y0tuoHilw /¡/
ꩽîM©
S®
©Míi°b3ZCZ& ?³êª|¯»3::tîtq³êª ö »3:tíiîP«b©7ªbi¥¥t2¢q{»Yz{
÷¬J
ëi»v£.¤qÕU*»Pq¤\
qq{..tSÊ»{tqqF*Mi¡tviYt.qM. i CUqMéMMqfq5¢YMq¥i.CUt¡C{qiiMi¥7¥t.i¤qz.©
Ó.z2ÔUê«ûÍ2ç±»7Kiëtît*qb.¤qÕU*{izqÉUtÔiY{i i.zUC i9iU¥t{qCiUMUzd¥iF¢k{U±êGO{»
íKiîGq©PGFO{uO{qiqCM»Ó{iqz f*C¤q{©GqéqqCiqM{ tP×qqqMq¥ÏÏ{CÉ{CUi¦t{i iCqUC
iúCUqM£×q {C{¼MMqftéMi.¥iɺi {z©^®¤qq×qqF*Mi¼iútU¥iq.tU{i i.zUC tGqUS
iCÎCiÉ¢q{P*qqCiqM{©
S®
©)Ki° ?qUbqi {P¤qCbqtUM5Uq¥¯P°±³²±³´a°¯.µ!¬ ?© MfÎqMäY.*UtqUéÎtqUtU
qq*¶&© F* i¤qzqiSi»P¸·© F*M*{CUt«iq¦-
Å
©¼°d*qQ¹º>»{Í2qiiMi¥¨¥iCi¤q¦i<©
F*ZÕ{M{*fU
/¡/
©b ?¼ÔMbÍ2nY{Méi© z{qÁê¼ÊîÉfqtÎtUi¥T7{Mi.fU-
Å
©½°C©
?.* MúiÔiYUMiÏ¥iCi¤qÏM`.
*°Ð d*q.iqÎi*»izÏËviC
*°dYdqdi.CUiÏC¤qq¥iCi¤qÏi
*©
½k ¾ ¿z^v Ô !q^Z&³P¿¨& !^
ª`gÀ ú*qC`iqUMMq{ibiCÎ z{×qqiÂ.
/¡/
Í5Îq¤qM{g* i×qqF*Ciq©
ª`bÖ£ ÁÔ¯i
ø
¯©
¯©_¯°« ?5 U«M|À|»PUnΤqq{z*T5s±*z*.tq. i.i5b»Ó½È*zÖ*Í5SYÎn*CUiC
5@Á|Ö5sÂiC.{M*é*I5f» *±ÈÃ9¬* ¹ *Ã*ziÄ`tU«tÈ
*Ãd {Mq¥f*zq¤qt-fiÅ)Å
* /1/
°
i£*°.»d È ¬ *! * ¹
/¡/
*qÖ!Í5SY`*CUÔqi#z{¥iq{C*½i. Mqq¤q{½ÁȾt * æ
* ð
{kÈ
Ã
©ô.¤zqZq¤zUÆ i* Mq¤qCM*
ð Æ
UÓ*iC.Mi±.{© ?Æ Mi¨.¤zqZq¤zUi
* M`¤qq{z*$Æ"Çq.iMUSz¤q..¤zqZq¤zUiP*ÄqU2¡{iiUzCÆ © ?Âi`Æ2ÇÔU
,
¤qtz*
Æ ÈÊÉ
¶
°Ò@*©£&i .¤zqZq¤zUÆ t3*Äq{qT** Æ *zMi¥i«iPÆ M *©
¾ ¿z^v s ocF5¬*!*¿¹
/¡/
rjoCyri nilw.ojy0t.`0f0tkilwÀ$IËo;`0f0tk̤ilhCÍ#ß_Ø.Ø&áCÛZàßUákØSÚ0
cf
®
i~`ceogt0y0w7xgÎ f `q*EilhQoowy0w.vi~`ceotuoIoÏilhc>hy£m¥tuoghj¥;rkfv0¥;n>oHÆ f `Ðt0y0w7xBÑ
m
ilw9*Ehj¥N{
c>y&c.5y0w7ilhjohf0wÆ Ò}hj¥;{XyIkfv0¥Nn>oHÆ ilhV{jy&nln>ojv+y4ÚÊØ<áÛtÝUß)Ó{ÚþÐ`0f0t5Q
¯©ö ° ¾ ¿Z^ Ê oc£5sÔ¬C*gÔ!Ê*HÔ¹
/¡/
b
ÔÖÕ u×
p
bBrjo'cedgfØri nilw.ojy0t`0f0tkhBilw$À$ oc£*
rjoQ*
HÙ
* p
y0w.v+5Úrjo
5 qÙ
ø 5 p
°³ÊËog`0f0tkÛ5
ilhéáiÝUÞtÚ&\þCáißUàáiÝMÝÉâºà{Û7ÛiþqáiýYØcf+5
p
i~`+c>ot0o
oÏilhc>h+ykoc1y&rjf&nilÜotIÆ `0f0tQ5Ýhj¥N{Øcey&c Æ ilhqm¥tuoilw *b y0w$ilhf0kf0tÞm&ilhjkßUØ` tuf0kà{&È Ã
cf
{&ÈÃ
p
y0w.vBy0w9ilhf0kf0tÞm&ilhjkâá ` tuf0k Ëvt.
ã tt{ ÈÃ
°Ic1féËiC
ã
i\{ ÈÃ
p
°Hd}&i {hy&ceilh¡` 'c>ocedgf
`0f&nln>f0d}ilw7|{jf0w.v0i c>i f0w7hä
©0¯¬Æ Ò'{&È Ã æ"#
e=
¸ U
e=
°C°
=@å
{&È Ã % b
©ö ¬æ
ÈÃ
Æ °jÇÊ°Pæ"#
>=
¸ á
>=
°.°
=å
Ëi.
aã
it ÈÃ ° %
b3d}otuogæBilhc>oQ¨¥;f&cei ow.c;ky m` t0f0kâ*IÃcf
ã
i\{ Èó
?@W
ö
.{
ö
©Uët°.°qC5¢k{¬
Y
%&ZÚç]£Ìnortuy0i {Q{jf&rjf0tuv0ilhjk6ilhVy0wSoj¨¥ily&n>ow.{jogt0on>y&c>i f0wSf0wTc>oChoc7À$
¯©Mëi°z&.i q5 iz»5
iq85
p
UM«iF5Y £?TGq{M{<¼t.|i.CZU{½*³.i
,÷¡ø
¯°<Í2iqq`*'Gz{M{Sé.¤z.i{ù
tqù
p
»i ?Î.MÎzUUMq
å
iz
å p
©fªné¤zÄ`¤q<*M
*zq{×zqÉUt tÓtU¥iq.tUi i.qM.©VÏ¥t{q.iMO*Mi¦i^qQ{<¢ztUC`Í2ªn¢Mqq{i<½i
q{tYiCqM.t\*iM|U'W{ë
C{
ëi©_¯
®
°C°.¬
èPé& !^ _`
å
y0w.v å p
y0tuo{jf&rjf0tuv&y0w.cÐhjilkCm3n>o9nilw7xhjbceowê5´æë5
Ù
ø 5 p
y0h^y
kocy&rjf&nilÜotL
ì+íïîزFð§ñòÓª`Öé
Sø
¯°
c » *qi
ÔlÕ u×
p
»qÈ7Ôæ25sÔjÁéÖ5sÂÔ MYqúM*{C.{n*MiÎi.¾iQ-
c ù;Ô_°C»
{&È Ã
Ô
Mf*zÔMÎt¥i£i£-
c å
ÔG°UØ-
c
ù;ÔG°éiq
ã
itYÈ Ã
Ô
MM.iiCqqM*ó-
ciokp
å
ÔS°.©ØGz±i
.zq{CUi@MUqC»@YT*9{qÈÃ
Ô
tq
ã
i\{ ÈÃ
Ô
i.O{.i»@tq±{tqqF*Miq©0¯éiz±{©ö M¦q{×qzÉUi
¯T©
ö
°Ð¢ZizUCq©¡Ë z{q»Ói«.zq{CUi9UMq.»?À ÉCÎi.CZUT*{$Gq{M{<i.i.iM¥iq.iM{tUF
{tYiCqi*»tq.{5¢k9qS¢ZiM.nÍ2ª`¢YMq.F*.Mi¡t {i i.zUCΩ
?|qqi Í2.zq{CUiP{iC{»^*z*i iMi¥½tq{i iCqUC MqUM{ *z«*qC{<*.M`Ut¨i
5
iØkÈ Ã
MM.iiCqqM
i
/1/
° **qÎ.S*CUn*Mi¼is5
p
i$&È Ã
p
FU{i<7*Â2q{2
FÏqM.`*FÊ» tq½É£UiM.¦MÎzUM{½ *qÎt.£¥iq{CiÓq.i iCÉUi
ëi©_¯
®
°.°C©¨Ë zUz{{.CiS
{tqqF*Mi¨t{i iCqUC MzÎUqMM{ *¦qin«*q5 qÙ
ø 5 p
UúÀ F.ÎiC.{M*|
® »
q¤\±iqqF*Mi£©0¯fMÏq×qqF*Mi
¯T©ö °C© Ë qÓi iUt¥¡iZ*z{tYiCqM. iUCMÎzUM{vqd*q
MUqMq¥Îi.iÂËviC
-
ciokp
å
ÔG°C°i.«M.iiCqqM{©bË qMfq{..tS¨{izqÉUt¡i i i.qM.ãU
{t*iMq{¡U| iU{©
ö
ivz{×qqF*Mi
¯©
ö
°.©
¯©)(i° Ë qÄ`i C{.¤zÉéik*qM@iCÏU@q{iC{
ö
qC5¢k{¡U'Wë
C{
ëi©_¯
®
° tq
ëi©_¯ëi°.°C¬
Y %&ZôP]
oc å
y0w.v å p
rjoIc>dgf+{jf&rjf0tuv&y0w.c;hjilkCm3n>oInilw7xh_`
å
y0w.v å p
y0o
,÷|ø
¯°õ
{jf0w7w.oj{cojv.oi~`0otcPhj¥tÞ`0y&{johù
y0w.vù
p
d}i c>@¥w7ilkfv0¥;n>y0tI.oi~`0otc`0f0tkhI5
y0w.vV5
p
bc>ow$5
ilh
y&nortuy0i {jy&nln'{jf&rjf0t0v&y0w.ccfQ5
p
ì+íïîزFð§ñòÔªnQAéY
®
iÔ¯© ªn£¤zé.¤zqYt.q
å
ÔbM¡.MÎzU£×zY.{#UMq iq#M`Ïù;Ô
é
l÷ø
¯°<Í2{tqq{n*±×q {iÔ×qqC*MiU;Ô@¬È mnci·kp
ò å
ÔP¹ È p
q{z» *zIGqUSiCö5sÔ
iC.{M*Â*ÂùÔM¤qqMZq¤zUiC©
ã
i¢k{C.Éi»úU
֐J
ë|iq MÐ5sÔúM¤qqMÎq¤qMiú*z{
å
Ô U
.MqM×q {C{ÂUMq
.{ÔêM ÍGÀ »N::iî2qiq©ª»Wëi»q©_¯i¯íi°C©
Gqi»zq{iC{ ö MÎzUM{C¬
Y %&ZöôP÷] oc
å
y0w.v å p
rjoBc>dgfVhjilkCm3n>ospsrjotuojv'nilw7xhy0ilw7Ôù
y0w.vÎù
p
y0h
l÷±ø
¯°õ
{jf0w7w.oj{cojvIpsrjoth'f `|v0i~øCot0ow.c>i y&rn>oHpsrtuy&cei f0w7hVU
y0w.v|U
p
_`
å
ilh@{jf&rjf0t0v&y0w.cHc1f å p
bceow ceo
.oi~`0otcF`0f0tkhD5
y0w.vQ5
p
bgy0hjhf{i y&c1ojvtuoh¡m;oj{c>ilon'c1fù
y0w.véù
p
bgy0tuoy&nortuy0i {jy&nln{jf&rjf0tuv&y0w.c1
¯©)i°£ùf.Mq¥ÔUiC.M{i`qqivC¤q.¥t{Si»qqC2¢qM'W0( . (i©)(i° iq (i©)i°C°.¬
Y
%&Zú3]
oc
÷
rjostuojy&cotQf0toj¨¥;y&n7c1fëzy0w.vn>oc å
y0w.v å p
rjoDc>dgf
ö
÷ø
¯Qv0ilkow7hji f0w.y&n
hjilkCm3n>o+nilw7xh_`c>o.oi~`0otcN`0f0tkh5
y0w.vB5
p
by0hjhf{i y&c1ojv'c1fBhf0ko
l÷7ø
¯T°õ{jf0w7w.oj{cojvV.oi~`0otc
hj¥tû`0y&{johù
y0w.véù
p
f ` å
y0w.v å p
bgy0tuoy&nortuy0i {jy&nln{jf&rjf0t0v&y0w.cc>ow å
ilhV{jf&rjf0tuv&y0w.ccf å p
¯©Mìi°D9.tYiCÉUt
ëi©_¯
®
°.» qU2 q{«qTΤq.
t«.{iCt¨M
ëi©_¯
ö
°C°iYYq{CUi
*zGz{M{SiC.»¥iF¢k.¬
Y %&ZÝüP] oc
å
y0w.v å p
rjoc>dgfB{jf&rjf0tuv&y0w.chjilkCm3n>onilw7xh_`Ð5
ý
tuoh¡m3s5
paþ
ilhQyD.oi~`0otc
`0f0tkÿy0hjhf{i y&cojvc1fy0w7
l÷ ø
¯°õ{jf0w7w.oj{cojvÐ.oi~`0otLchj¥tÞ`0y&{jo`0f0t åQý
tuoh¡m3
å
paþ
bceow5 ïÙ
ø 5 p
y0h
yHkocy&rjf&nilhotqÆ hj¥;{zcey&cÆ ÒD{&È Ã æ2#
e=
¸ U
>=
°.°
=å
kÈ Ã
%
b<d}ot0oU$ilhy0w+ilhf0kf0tÞm&ilhjk
rjoc>dgojow9{&ÈÃ
y0w.v{&ÈÃ
p
@Y³^ §Z
ö ©®
°bª`Q5
tq95
p
b?ÔiM¥i{z.iM{iMF#i i.qt*éiCÎC»Un5¾Y*qiC 5 sÙ
ø 5 p
q×qq{³iT* æ * Ù
* p
iq³È¾Y5¤Á$Ö£5©$ ?±*zU.`Ui¦Âz.5¢k|qCiYt.F*Mi
ö
©_¯°
qM2.q5éqÎ*q±tU¥iq.tU¡{i i.zUC `?{5
iqÊ5
p
iMM2Ô¤q¼q{C{CU ¦ÈE
*zU2qi.t`*.)O{Ut$i«ÈôMÔ¤zqqi{i9#qC5¢kÎq{t.{ ë
.9W0(t°.©¿ª`Æ »DUtqÊá
¦iÏU
¯©
ö
°.»UnzÎ ¦.
*°£iz ÁY¦C
{&ÈÃ
°C©ãË qÄq×qqF*Mi
¯©
ö
°ÏMqUM{q
æÄ.
ÈÃ
ÆÄ°.°9æ
p
m
.
ÈÃ
*°C° iqÂ.
Æ °Óæ Á
æ Ñm ©
À$¤q.dqtUM5Uq¥z*Utq.¬úMMÐt*.¤zq.ni<*$z{qqC¤qqZz¤qU
iP*»¥t{q.{Â*© ?³Ubi7.¤zqZq¤zUiP* *qq¬
|æ"#
=9å
*
¦¦
È
>=
¸
°9æ
®
å %
-iÅeÅ
*Ôñ
¸0/1/
°9æ2#ʲ
å * Ã
¦¦
²
°Pæ
®
å %
ç±iC{5¢kM
p
tq
m
i. ?Ï.¤qqq¤qM{«i*»viSqi¥iiziiÈP»&z{qé
p Ù m
*z{M
iSqi¥itqiM° qUC{néC¤q©
!ÐZ Z #" oCy0oäÐÈ Ã
*°Ò±È Ã
ÆÄ° Ç æ È Ã Æ
°
$ð§°N°%n© ªn&ÏYÐq.izÔi{&È
Ã
iq
Ð*zCiqiÈ
Ã Æ °.©£fgÆ M În*i iMO{
iȦqU2¡¤qM×qUMb{iqzÉUiÂ{©_¯«U
¯©
ö
°q5¢k{¬
.
{qÈ Ã °æ
ö
.
Æ Ò {kÈ Ã °æ
ö
.
&È Ã °æ
ö
Z» .
È Ã
*°C°æ
ö
iqC
Æ
°Îæ
Á ö z©£-f{qIÆ
æ Æ Á¬{&È Ã ° Ç iq¡È à Æ
°'¿È Ã
*°ÒÈ Ã Æ ° Ç ©
ç±iC{5¢k.»ÈÃ
Æ °£MÏi×qqF*¦Mqq`§ U¤-fiÅ)Å
* ñÆ /1/
°.©f|-iÅeÅ
* ñÆ /¡/
°ÔUÏ
q¤qC.¤qqq¤qMtÐ* Ã »^Î¥i`È Ã Æ ° Ç æ6-fiÅ)Å
* ñÆ /1/
°.©zGqÂMÐÈ Ã
>=
° å È Ã
ÆÄ° Ç »q{
ÈÃ
e=
¸(
°9æ
®
i tU
U'Æ
iq
=
MbM'Æ
© )
GqMq{«ÈÃ
Æ °ÐMÐt^×qqF*fUqz`§UÏÈÃ
Æ °jÇÊ» iqiCÉ
ÈÃ
Æ °jÇi°
ð È Ã Æ °+*
æ ,
ÔlÕ
p ð
¼§Ô /¡/
q. ¼§Ô 弶-
ò #
®&%
iq+¼§ÔqF¢Mqм§Ô
·kp
fqq`§Y{M¤qq9*qÓ*z{.b`§YMSÐiU*¥i{
.¤z2
*z¼§Ôæ ¯«tAdæ ¯
¸³¦³¦³¦T¸
°.©
èPé& !^
ËoHhj¥;rkfv0¥Nn>o Æ ilhm¥tuoCilw *i~`y0w.v|f0w.ni~`fÈÃ
Æ
°Pæ ÈÃ
Æ °³
$ð§°N°%n©ÀÁC¤qq i.9*qT Æ MÐq¤z.M *©ÐÐÆ ÒV{&ÈÃPæ2¢
U°Óqid.iz.Z»Ê*qf.iqi
ÆöÁ@{&ÈÃPU
Á ö Z©ÐGqÆàÁ'kÈÃ9MÓiY×zqÉUqz`§ÂMBÆ
©Ðªn
=
bMÆ
Ê*z{.n§MSÐ
i.F*F¢k«M*{¥t{£¹£C¤q2*qD¹
= æ ?
Á@Î7»z{.
?
MúU|kÈ
Ã
»Î M U|Æ Y. Î æ ¹
=
©ÐGqMq{
Æ UÐq¤q.«M *q{
=
MúU Æ »Y.*z{.`§YU<*
?0/
MkÈÃÐ.¤q2*qT
= Á
?0/
MúUÆ ©£UqtUF
ÈÃ
e=
°9æ¿ÈÃ
>=
Á
?1/
° å ÈÃ
Æ °C»iq¡ÈÃ
Æ
°'¾ÈÃ
Æ °.©ûú¤\IÆ '"Æ
CÎÈÃ
Æ
°9æ ÈÃ
Æ °.©
À$é.¤qq iC*qÈ Ã Æ °æ È Ã Æ
°.©I@UCSqC2¢qf*z Æ
Mq¤qCM *©ªn32ÏYU
Æ
F* 2æ"¹
=
q{C
=
MÐM|*¿iq+¹UÓé i.F*F¢kU*¥i{C©£Gqfq{C`§YMS
?
UB&ÈÃÓ.¤z2
*z¹
=
æ42gÁ
?
©C tfiM7Î MÆ q5¢kéÈ
¹ = ¸
Î7°ÐæÈ
2gÁ
?¸
Î7°Óæ
®
»vC£È
e=
¸
Î7°dæ
®
iq
=
UM$Æ
©655qC2¢q*qÈÃ
Æ
°fæ ÈÃ
Æ °UqMM{ Æ æ Æ
©Ôª`62Ï U^Æ
©£ ?
ÈÃ
2\°dæ ²*q.`§YMS*}Î UÆ .¤q2*zÈÃ
Î7°9æ ²Y©£Gq72
ø Î æ ?
MUz{kÈÃ.»Yiq 2æ Î
MbM Æ ©£@UziUFÊ»CUz{ Æ
Mq¤qCM * iq Æ ' Æ ¥in Æ æ Æ Mq¤q.M *© )
ûvÂq×qqF*Mi
¯T©ö ° Æ MÓq¤q.bM *» CéM{
ö ©®
°ÓtqÔqCi i.F*Mi
ö ©®
°.»&iqz»YiqqF*Miq
{©_¯«iq|{©ö MÂq{×qzÉUi
¯©ö ° MqÉÔ*q
ã
i\{ È
Ã
UM.iiCqqM
/1/
m98
Ù ,
ÔlÕ
p
/1/
ð
¼§Ô /¡/
° m ©
ö
©_¯°sèY3é& !^v
ËotuoQoÏilhc>hy|rjy0hjilh:½æ"#0ÎÔ
¸
Î$Ã
Ô ÔlÕ
p
×;;;×,
·<8
%
f `H*Rhj¥;{^c>y&c1ä
= C#0ÎÔ
ÔlÕ
p
×;;;×,
·<8
%
ilhVy+rjy0hjilhVf `qÆ b
> C#0ÎÔ
¸ Î Ã
Ô ÔlÕ
,
·kp
×;;;×,
·<8
%
ilhVy+rjy0hjilhVf `q&È Ã y0w.vI#0Î Ã
Ô ÔlÕ
,
·kp
×;;;×,
·<8
%
ilhVy|rjy0hjilhf `q&È Ã b
?
Qc>oChj¥Nrkfv0¥;n>oh7eÎÔ
¸ Î Ã
Ô ¸ ÔÖÕ
p
×;;;×,
·<8
Ògy0tuof0tceff0w.y&n§`0f0tÈ}b}i loläs* æ
pA@
Ô @ ,
·<8
eÎÔ
¸ Î Ã
Ô
b
B
Hd}ow ÔÖÕ
p
×;;;×, ¸ È
ÎÔ
¸ Î Ã
Ô
°Óæ ¼§Ôj
¾
¿z^v
7¥;{Xy|rjy0hjilh ilhV{jy&nln>ojvByffv|rjy0hjilhf `g*ày0hjhf{i y&c1ojvBc1fQÆE
Ë qiC´ÈºæE5¬Á¼Ö5  MiF2Yi±n¢k¨iC©ç±iC{5¢k.»^q{Ôq¼§ÔÐiCéqÔ¥t`
*ztUM5Uq¥Î{t.iMUtSY¬
bv #" owØc>og¼§Ôqy0tuofv&v0bsc>oqilhf0kf0tÞm&i {D{n>y0hjhf ` ÈTilhqilowØrHÎ æ C
*°y0w.v
c>oCilhf0kf0tûm&i {{n>y0hjhf `
ã
i\{ Èó
$ð§°N°%i z.i i.F*Mi
ö ©0¯T°.©¼ ?
ö ©®
°fÔq5¢kÏ.{±*zÂÈ Ã
ÆÄ°
Ç
æß-iÅeÅ
* ñ
ÆC
/¡/
°C©
ª`@Æ
YÏt*qUC{nC¤qiqÁiqM{{i
Æ Ò {&ÈÃC°MÆÄ©Ë q{C¡n§F*Î7qiCU