ࡱ> Root Entry)@FileHeaderCDocInfo48BodyText ##!#" $%Root Entry)@FileHeaderCDocInfo48BodyText ##  ] ȩ : Topology of dimension 4 and disk embedding Ŭ : (̬ǘ P [mYP] | : 5 22|(|) $ 5:00-6:00 nj :  6218 Understanding topological manifolds of dimension 4 is fascinating but difficult subject. Embedding of flat 2-dimensional disks in 4-spaces is the key problem. I will introduce fundamental ideas related to this, particularly Casson, Whitney, and grope tower constructions in dimension 4, and report some recent advances about Casson towers and disk embedding. The talk will be aimed at non-specialists. ɻGIF89aɻxxxkkk]]]PPPCCC555((( d`LH00`Hذ̘`H0|pdXL@`0H `H0`dHL`H0xp`XH@0d LȰ``HH00dLؘȀ`H0xp`XH@d0L `H0d`LH`H0|pdXL@0`$H`dHL00`HذȘdL0xp`XH@0` HdH0ȳ``HHdL0xp`XH@`0H Ը̰ĠऀؘpȈXxHp@h@d8`8X0xT0pH dxddxd`d`p`|``x`p``x`!, H*\ȰÇ#JHŋ3jȱǏ CIɓ(S\ɲ˗0cʜI͛8sɳϟ@ JѣH*]ʴӧPJJիXjʵׯ`ÊKٳhӪ]˶۷<3e(w?t;._zc//E̸ǐ#KL2#мx?{4iѥOg:t֨Y~=ڵ`tv[oߣY[xճ.>7ͺyKWZسkfPћh}Od^^A~6`Ug^>c@Zafar!z!c%!!n!xa.#d zt|-Hff`kJؤl y0 $Cמ| H&}ʷg|w槠x)}N2X>夑yyK|&Y^c9uZj٪yvdǧPz[v*~t&{&YӞ *zk2j.&CkS$D.oB+ڹ,j*ęN]J[jb )6䬲-ovwI5SaxKEV wWL,}><{/B9^a+5E 73i3s3ov$0gl}. bT"30ȤgLa+2SbvFe?I ? KNgF2g("f٫r)! 8O.wϹE"`mlMW'ns}K0)Zpv^4q}Xsj*C L2lhR[ ?I>l9[&풿K[Q?暘.C usf|C+:h bR V78AjZ\@B]:5{=<;u$y |= cWnCv ;F)lĥp>"Cw5)晑x Fp#]-V*q12Vq)^4:eQe.bQ%ſ/şm2&(fBy!6Һ]!<}F;\Vw-UL9mk)\ulm^VgXVjʎ%u@DO 6C,H,#GB!k0~ 6*7=M*Z:ҙ#?*?ӿT@Y~X+mj3'm[v|:j)%C$Mϼ5#cd߈:\Users\ajou\AppData\Local\Temp\prv00000db41f64.gif(PF;F m 8\sjw8A '3O8jw3O8\TFZF=F@;յuduAuZFbAuduZFJşuZFZF*ڟuZFğu\TFduAuXTFbAuduXTF0+u4Ɵu0odu k`ޚ TLXTFpohkSection0XdiTTMHTQ>S-B}?*Õ/!D?EbrѢE`M2)EBP-[ ;7qw9{9#ȁ,Y;긶M^,kh^*[1'+Nṙ>km3eڶ-5S}'N"];/@4{eYAϢ?!Uf-Ks!cL Uz\#'>7!rGS.6LtfMͥNG6xtmcQ O(K 7A8~W[m7#eVBVA?@ABGDEFHJKNOPQRSTUWXYZ[\]^_`abcd  !"#$%&'()*+-./012356789:;<=>?@ABGDEFHJKNOPQRSTUWXYZ[\]^_`abcdHwpSummaryInformation.,PrvImagePrvText.DocOptions g)g)Section0VScripts g))JScriptVersion L DefaultJScriptI_LinkDocM  ] ȩ : Topology of dimension 4 and disk embedding Ŭ : (̬ǘ P [mYP] | : 5 22|(|) $ 5:00-6:00 nj :  6218 Understanding topological manifolds of dimension 4 is fascinating but difficult subject. Embedding of flat 2-dimensional disks in 4-spaces is the key problem. I will introduce fundamental ideas related to this, particularly Casson, Whitney, and grope tower constructions in dimension 4, and report some recent advances about Casson towers and disk embedding. The talk will be aimed at non-specialists. ɻGIF89aɻxxxkkk]]]PPPCCC555((( d`LH00`Hذ̘`H0|pdXL@`0H `H0`dHL`H0xp`XH@0d LȰ``HH00dLؘȀ`H0xp`XH@d0L `H0d`LH`H0|pdXL@0`$H`dHL00`HذȘdL0xp`XH@0` HdH0ȳ``HHdL0xp`XH@`0H Ը̰ĠऀؘpȈXxHp@h@d8`8X0xT0pH dxddxd`d`p`|``x`p``x`!, H*\ȰÇ#JHŋ3jȱǏ CIɓ(S\ɲ˗0cʜI͛8sɳϟ@ JѣH*]ʴӧPJJիXjʵׯ`ÊKٳhӪ]˶۷<3e(w?t;._zc//E̸ǐ#KL2#мx?{4iѥOg:t֨Y~=ڵ`tv[oߣY[xճ.>7ͺyKWZسkfPћh}Od^^A~6`Ug^>c@Zafar!z!c%!!n!xa.#d zt|-Hff`kJؤl y0 $Cמ| H&}ʷg|w槠x)}N2X>夑yyK|&Y^c9uZj٪yvdǧPz[v*~t&{&YӞ *zk2j.&CkS$D.oB+ڹ,j*ęN]J[jb )6䬲-ovwI5SaxKEV wWL,}><{/B9^a+5E 73i3s3ov$0gl}. bT"30ȤgLa+2SbvFe?I ? KNgF2g("f٫r)! 8O.wϹE"`mlMW'ns}K0)Zpv^4q}Xsj*C L2lhR[ ?I>l9[&풿K[Q?暘.C usf|C+:h bR V78AjZ\@B]:5{=<;u$y |= cWnCv ;F)lĥp>"Cw5)晑x Fp#]-V*q12Vq)^4:eQe.bQ%ſ/şm2&(fBy!6Һ]!<}F;\Vw-UL9m3O8\TFZF=F@;յuduAuZFbAuduZFJşuZFZF*ڟuZFğu\TFduAuXTFbAuduXTF0+u4Ɵu0odu k`ޚ TLXTFpohkSection0XdiTTMHTQ>S-B}?*Õ/!D?EbrѢE`M2)EBP-[ ;7qw9{9#ȁ,Y;긶M^,kh^*[1'+Nṙ>km3eڶ-5S}'N"];/@4{eYAϢ?!Uf-Ks!cL Uz\#'>7!rGS.6LtfMͥNG6xtmcQ O(K 7A8~W[m7#eVBVA