The wild world of 4-manifolds

Thisisapanoramaofthetopologyofsimply-connectedsmoothmanifoldsofdimensionfour.Dimensionfourisunlikeanyotherdimension;itislargeenoughtohaveroomforwildthingstohappen,buttoosmalltohaveroomtoundothem.Forexample,onlymanifoldsofdimensionfourcanexhibitinfinitelymanydistinctsmoothstructures.Indeed,theirtopologyremainstheleastunderstoodtoday.Thefirstpartofthebookputsthingsincontextwithasurveyofhigherdimensionsandoftopological4-manifolds.Thesecondpartinvestigatesthemaininvariantofa4-manifold--theintersectionform--anditsinteractionwiththetopologyofthemanifold.Thethirdpartreviewscomplexsurfacesasanimportantsourceofexamples.Thefourthandfinalpartofthebookpresentsgaugetheory.Thisdifferential-geometricmethodhasbroughttolighttheunwieldynatureofsmooth4-manifolds;andalthoughthemethodbringsnewinsights,ithasraisedmorequestionsthananswers.Thestructureofthebookismodularandorganizedintoamaintrackofapproximately200pages,whichareaugmentedwithcopiousnotesattheendofeachchapter,presentingmanyextradetails,proofs,anddevelopments.Tohelpthereader,thetextispepperedwithover250illustrationsandhasanextensiveindex.