Cohomology of Groups

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Cohomology of Groups

Cohomology of Groups

Kenneth S.Brown

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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.

類別:

Mathematics - Algebra

體積:

87

年:

1982

語言:

english

頁數:

305

ISBN 10:

0387906886

系列:

Graduate Texts in Mathematics

文件:

DJVU, 9.46 MB

IPFS:

,

english, 1982

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