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代数拓扑中微分形式

代数拓扑中微分形式

责任编辑:湖北美术出版社

发布日期:2021-04-22

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代数拓扑中微分形式

《代数拓扑中微分形式》内容为:Theuidingrinciplenhisooksoseifferentialormssnidnexploringomefheessigestiblespectsflgebraicopology.ccord-ingly,eoverimarilynheealmfmoothanifoldsndsehedehamheorysrototypefllfohomology.orpplicationsohomotopyheoryelsoiscussyayfnalogyohomoiogyitharbitraryoefficients.lthougheavenindnudienceithriorxposureolgebraicorifferentialopology,orheostartoodnowledgefinearalgebra,dvancedalculus,ndoint-setopologyhoulduffice.omeacquaintanceithanifolds,implicialomplexes,ingularomologyndcohomology,ndomotopyroupsselpful,utoteallyecessary.Withinheexttselfeavetatedithareheoredvancedesultsthatreeeded,ohatathematicallyatureeaderhocceptshesebackgroundaterialsnaithhouldebleoeadhentireookiththeinimalrerequisites.

章节目录

IntroductionHAPTERehamheory1heehamomplexnheehamomplexompactupports2heayer-VietorisequencehefunctorQheayer-Vietorisequenceheunctorndheayer?Vietorisequenceorompactupports3rientationndntegrationrientationndhentegralfifferentialormtokes’theorem4oincar6emmasheoincareemmafordeRham~ohomoiogyheoincareemmaorompactlyupportedohomologyheegreefropermap5heayer-Vietorisrgumentxistencefoodoveriniteimensionalityfehamohomologyoincar6ualitynnrientableanifoldheiinnethormulandheeray-Hirschheoremheoincar6ualflosedrientedubmanifold6hehornsomorphismectorundlesndheeductionftructureroupsperationsnectorundlesompactohomologyfectorundleompacterticalohomologyndntegrationlongheiberoincar6ualityndhehornlasshelobalngularorm,theulerlass,andhehornlasselativeehamheory7heonorientableasehewistedehamODplexntegrationfensities,Poincarduality,andhehomsomorphismHAPTERheech??dehamomplex8heeneralizedayer-Vietorisrincipleeformulationfheayer-Vietorisequenceeneralizationoountablyanypenetsndpplications9orexamplesndpplicationsfheayer?Vietorisrinciplexamples:computingheehamohomologyromheombinatoricsfoodoverxplicitsomorphismsetweenheoubleomplexndehamndachheic?tac-toerooffhefinnethormula10resheavesndechohomologyresheavesechohomology11phereundlesrientabilityheulerlassfnrientedphereundlehelobalngularormulerumberndhesolatedingularitiesfectionulerhara


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