
mapping cone (homological beejaganitam)

homological beejaganitamlo, mapping cone anedi topologylo saaruupya nirmaanam nundi prerana pondina golusu samudaayaala patamlo nirmaanam. tribhujaakaara vargaala siddhaantamlo idhi oka rakamaina combined kernell mariyu cockernal chain complexelu abelian vibhaagamlo vaati nibandhanalanu teesukunte, tadwara manam cohology gurinchi maatlaadavacchu, appudu mapp yokka cone "f" asyclic antey mapp anedi pakshika-isomorphism anie ardham; manam complexela yokka utpanna vargaaniki velthe, dheeni ardham "f" anedi akkada oka isomorphism, idhi samuuhaala maplu, ring meeda modules ledhaa ekapaksha abelian vargam yokka muulakaala suparichitamaina lakshanaanni gurtuchestundi, ayithe kernell mariyu kokernal rendoo adrusyamaite, mapp oka isomorphism avutundi. manam tii-ketagireelo pani chestunnatlayite, vaastavaaniki cone daani core vastuvula madhya myapla kernell mariyu kokernal rendintinee andistundi.
nirvachanam.
cone nuu edainaa sankalana vargampai (i.ii.dheeni padanirmaanaalu abelian samuuhaalanu yerparustaayi mariyu dheenilo manam edainaa rendu vastuvula pratyaksha mottaanni nirminchavacchu). suutram _ 1 rendu sanklishtaalu, differential suutram _ 2i thoo undanivvandi.ii.,
mariyu adevidhamgaa suutram kosam _ 4
complexes formula _ 5 yokka mapp kosam, manam cone nuu nirvachistaamu, tarachugaa formula _ 6 ledhaa formula _ 7 dwara suuchimchabadutumdi, idhi krindi complexes gaa untundih
bhedaalato
ikkada suutram _ 10 anedi suutram _ 11 mariyu suutram _ 12 thoo kuudina sanklishtata.
suutram _ 13 paie bhedam suutram _ 14 paie sahaja bhedaaniki bhinnamgaa undani mariyu kontamandi rachayitalu vaerae sanketha sampradaayaanni upayogistaarani gamaninchandi.
anduvalla, udaaharanaku mana samudaayaalu abelian samuuhaalaku chendinavi ayithe, bhedatmakata ilaa panichestundi
aastulu.
ippudu manam abelian vargampai pani chestunnamani anukundam, tadwara oka sanklishtata yokka homology nirvachinchabadutundi. cone yokka pradhana upayogam pakshika-isomorphismlanu gurtinchadam cone asyclic ayithe, appudu mapp pakshika-isomorphism. dheenini chuudataaniki, manam tribhujam yokka unikini upayogistaamu.
ikkada myapla suutram _ 17 pratyaksha saaraamsaala dwara ivvabadutundi (golusu samudaayaala yokka homotopy varganni chudandi). idhi oka tribhujam kabatti, idhi homology samuuhaalapai sudeergha khachitamaina kramaanni istundih
mariyu suutram _ 13 asyclic ayithe, nirvachanam prakaram, paina perkonna bayati padaalu sunna. eee kramam khachitamainadi kabatti, dheeni ardham suutram _ 20 anni homology samuuhaalapai isomorphismnu prerepistundi, anduvalla (mallii nirvachanam prakaram) idhi pakshika-isomorphism.
eee vaastavam abelian vargamlooni isomorphisms yokka saadhaarana pratyaamnaaya lakshanaalanu kernell mariyu cockernal rendoo adrushyamayye pataluga gurtuchestundi. oka cone yokka eee roopaanni oka ummadi kernell mariyu kokernal gaa anukokunda kanipinchadu; vaastavaaniki, konni paristhitulalo cone aksharala rendintinee kaligi untundi. udaaharanaku, manam abelian vargampai pani chestunnamani cheppandi mariyu formula _ 1 degree 0 loe oka nanziro padam matrame kaligi untundih
anduvalla suutram _ 24 kevalam suutram _ 25 (antarleena abelian vargamlooni vastuvula patamgaa). appudu cone kevalam
(under sett text prati padam yokka degreeni suuchistumdi.) eee sanklishtata yokka homology appudu
idhi pramaadavasaattu jaragadu mariyu vaastavaaniki prati tii-ketagireelo jarugutundi.
mapping cylinder.
sambandhita bhavana mapping cylinder suutram _ 30 anedi golusu samudaayaala yokka padanirmaanam, suutram _ 31 anedi sahaja patam. f" yokka mapping cylinder nirvachanam prakaram "g" yokka mapping cone.
sthalashaastra prerana.
eee sanklishtatanu sthalavignaana sthalaala suutram yokka nirantara patam yokka mapping cone (topology) kuu saaruupyataloo cone anie pilustaaruh sthalavignaana cone suutram yokka yeka golusula sanklishtata "x" nundi "y" yokka yeka golusula prerita patam yokka cone (golusu-sanklishta-senslo) kuu samaanamaina samaruupata. complexela mapp yokka mapping cylinder adevidhamgaa nirantara myapla mapping silindertho sambandham kaligi untundi.

