02453nam a22003378i 4500001001600000003000700016008004100023020001800064020001800082035002000100041000800120082001500128100003100143245006900174264007100243300003800314336002600352337002600378338003600404490005900440500001300499505037000512520096400882650003001846650002101876650002001897856005501917932003201972596000602004949010502010CR9780511550256UkCbUP090511s2003||||enk o ||1 0|eng|d a9780511550256 a9780521537490 a(Sirsi) a791516 aeng00a514/.22211 aJohnson, F. E. A.,eauthor10aStable modules and the D(2)-problemh[E-Book] /cF.E.A. Johnson. 1aCambridge :bCambridge University Press,c2003e(CUP)fCUP20200108 a1 online resource (ix, 267 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier aLondon Mathematical Society lecture note series ;v301 aenglisch0 a1. Orders in semisimple algebras -- 2. Representation of finite groups -- 3. Stable modules and cancellation theorems -- 4. Relative homological algebra -- 5. The derived category of a finite group -- 6. k-invariants -- 7. Groups of periodic cohomology -- 8. Algebraic homotopy theory -- 9. Stability theorems -- 10. The D(2)-problem -- 11. Poincare -- 3 complexes. aThis 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field. 0aLow-dimensional topology. 0aHomotopy theory. 0aGroup algebras.40uhttps://doi.org/10.1017/CBO9780511550256zVolltext aCambridgeCore (Order 30059) a1 aXX(791516.1)wAUTOc1i791516-1001lELECTRONICmZBrNsYtE-BOOKu8/1/2020xUNKNOWNzUNKNOWN1ONLINE