内容简介 DeRhamcohomologyisthecohomologyofdifferentialforms.Thisbookoffersaself-containedexpositiontothissubjectandtothetheoryofcharacteristicclassesformthecurvaturepointofview.Itrequiresnopriorknowledgeoftheconceptsofalgebraictopologyorcohomology.Thefirst10chaptersstudycohomolgyofopensetinEuclideanspace,treatsmoothmanifoldsandtheircohomologyandendwithintegrationonmanifolds.Thelast11chapterscoverMorsetheory,indexofvectorfields,Poincareduality,vectorbundles,connectionsandcurvature,ChernandEulerclasses,andThomisoorphism,andthebookendswiththegeneralGauss-Bonnettheorem. Thetextincludeswellover150exercises,andgivesthebackgroundnecessaryforthemoderndevelopmentingaugetheoryandgeomtryinfourdimensions,butitalsoservesasanintroductorycourseinalgebraictopology.Itwillbeinvaluabletoanyonewhowishestoknowaboucohomology,curvature,andtheirapplications. | |