Cohomology of Groups

ThisbookisbasedonacoursegivenatCornellUniversityandintended

primarilyforsecond-

yeargraduatestudents.Thepurposeofthecoursewas

tointroducestudentswhoknewalittlealgebraandtopology10asubjectin

whichthereisaveryrichinterplaybetweenthetwo.ThusItakeneithera

purelyalgebraicnorapurelytopologicalapproach.butratherIuseboth

algebraicandtopologicaltechniquesastheyseemappropriate.

ThefirstsixchapterscontainwhatIconsidertobethebasicsofthesubject.

Theremainingfourchaptersaresomewhatmorespecializedandreflectmy

ownresearchinterests.Forthemostpart,theonlyprerequisitesforreading

thenotesaretheelementsofalgebra(groupsrings,andmodules,including

tensorproductsovernon-commutativerings)andtheelementsofalgebraic

topology(fundamentalgroup,coveringspaces,simplicialandCW-

com-

plexes,andhomology).Therearehowever,afewtheoremsespeciallyin

thelaterchapters,whoseproofsuseslightlymoretopology(suchasthe

HurewicztheoremorPoincaréduality).Thereaderwhodoesnothavethe

requiredbackgroundintopologycansimplytakethesetheoremsonfaith.

Thereareanumberofexercises,someofwhichcontainresultswhichare

referredtointhetext.Afewortheexerdsesafemarkedwithanasteriskto

warnthereaderthattheyaremoredifficultthantheothersorthattheyrequire

morebackground.

Iamverygratefu1toR.Bieri,l-

P.Serre,U.Stammbach,R.Strebel,and

C.T.C.Wallforhelpfulcommentsonapreliminaryversionorthisbook.