Differential Topology

Exploringthefullscopeofdifferentialtopology,thiscomprehensiveaccountofgeometrictechniquesforstudyingthetopologyofsmoothmanifoldsoffersawideperspectiveonthefield.Buildingupfromfirstprinciples,conceptsofmanifoldsareintroduced,supplementedbythoroughappendicesgivingbackgroundontopologyandhomotopytheory.Deepresultsarethendevelopedfromthesefoundationsthroughin-depthtreatmentsofthenotionsofgeneralpositionandtransversality,properactionsofLiegroups,handles(uptotheh-cobordismtheorem),immersionsandembeddings,concludingwiththesurgeryprocedureandcobordismtheory.Fullyillustratedandrigorousinitsapproach,littlepriorknowledgeisassumed,andyetgrowingcomplexityisinstilledthroughout.Thisstructuregivesadvancedstudentsandresearchersanaccessiblerouteintothewide-rangingfieldofdifferentialtopology.