
nalikatmak parisar

ganitat, gulgulit manifoldchya submanifoldcha eka nalika parisar mhanje tyachya bhovati samanya bandalsarkha disanara eka khula sanch asato. 
nalikanchya shejaryamagil kalpana eka sopya udaharanat spasht kelee jaau shakate. swa-vichchhedananshivay samatalatil gulgulit vakr vicharat ghya. vakrareshevaril pratyek binduvar vakrareshevar eka resha kadha. vakr saral nasel tarr yaa resha ekmekanmadhye ekapeksha jaast guntaguntichya paddhatine chhedatil. tathapi, jarr konee vakrareshebhovati keval arund pattyamadhye pahile tarr tyaa pattyatil reshanche bhag chhedanar naheet aanee antar naan thevata sampoorn pattyala jhaktil. haah band eka nalikatmak parisar aahe. 
sarvasadharanpane, 's' heey 'm' chya anek patanche up-gunakar asoo dya aanee 'n' heey 'm' madheel 's' chey samanya bundle asoo dya. yethe 's' vakratechi bhoomika bajavate aanee 'm' vakr asalelya pratalachi bhoomika bajavate. naisargik nakashacha vichar qaraa
jeey "aine" chey shoonya vibhag sootra _ 2 aanee "emm" chey submanifold "ess" darmyan eka bijective patravyavahar sthapit karate. yaa nakashatil vistar 'jeey' chaa sampoorn samanya bundle 'aine' paryant, jyachi moolye 'emm' madhye aahet, asey sootra _ 3 haah 'emm' madheel khula sanch aahe aanee 'jeey' haah 'aine' aanee sootra _ 3 madheel homomorphism aahe, tyala tubeler neberhood mhanatat.
byavachada ekhadi vyakti swatah 'jeey' aivaji open seet sutrala 'ess' chaa eka nalika shejari mhanato, heey spashtapane gruhit dharale jaate qee homomorphism 'jeey' mapping 'aine' teey 'tii' astitvat aahe.
samanya nalika.
gulgulit vakratesathi samanya nalee hii serve diskche asey millen mhanoon paribhashit keleli eka anekpat aahe qee
aupcharik vyakhya.
sootra _ 6 gulgulit anek putt asoo dya. sootra _ 8 madheel sootra _ 7 chaa eka nalika shejari eka vector bundle sootra _ 9 aahe, jyamadhye eka gulgulit nakasha sootra _ 10 aahe, jenekarun
samanya bundle haah eka tubeler neberhood aahe aanee dusya bindumadhil defiomorphism sthitimule, serve tubeler neberhoodche pariman samaan asate, mhanje (vector bundleche pariman manifold manale jaate) sootra _ 20 chey asate.
samanyikaran.
gulgulit manifoldschya samanyikaranamule niyamit parisar kinwa poinkere jagansathi golakar tantunsarkhya nalikeey parisaranche samanyikaran hote.
yaa samanyikaranancha vapar samanya bundleche anuroop tayar karnyasathi kinwa tyaeivaji sthir samanya bandalsathi keela jaato, jeey sparshika bundleche pratisthapan aahet (jeey yaa jagansathi thet varnan swikarat naheet).