The Fibered Isomorphism Conjecture for Complex Manifolds  

作　　者：S.K.ROUSHON 

机构地区：[1]School of Mathematics,Tata Institute,Homi Bhabha Road,Mumbai 400 005,India

出　　处：《Acta Mathematica Sinica,English Series》2007年第4期639-658,共20页数学学报（英文版）

摘　　要：In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.

关 键 词：Complex projective variety Complex surfaces Whitehead group Fibered isomorphism conjecture Negative K-groups 

分 类 号：O174.56[理学—数学]