
tharsttan deerghavrithaakrithiyilulla anumaanam

vilyam tharsttante deerghavrithaakrithiyilulla anumaanam parayunnath parimithamaaya adisthaana groupulla oru clossed 3-manifold golaakrithiyilullathaanu, athaayath.iii. sthiramaaya positteev sekshanal vakrathayude oru remanian metrik undu.
mattu oohangalumaayi bandhappettava.
sthiramaaya positteev sekshanal vakrathayude remanian metrik ulla 3-manifold 3-golathaal moodappettirikkunnu, koodaathe covering parivartthanangalude group 3-golatthinte isometrikalaanu.
yadhaartha 3-manifoldinu vaasthavathil oru nissaramaaya adisthaana group undengil, athu 3-golatthinu (covering mapp vazhi) homomorphic aanu. athinaal, deerghavrithaakrithiyilulla anumaanam theliyikkunnathu poincare anumaanam oru anantharafalamaayi theliyikkum. vaasthavathil, deerghavrithaakrithiyilulla anumaanam yukthiparamayi rund lalithamaaya anumaanangalkk thulyamaanu poincare anumaanam, golaakrithiyilulla space phoom anumaanam.
deerghavrithaakrithiyilulla anumaanam 2003ll jii. theliyikkunna tharsttaninte jyaamitheeyavalkkarana anumaanathinte oru prathyeka kesaanu. perelman.
paraamarshangal.
anumaanangalude thelivinaayi, jyaamitheeya nirnaya anumaanathekkuricho poincare anumaanathekkuricho ulla lekhanangalile paraamarshangal kaanuka.

