Article
The fibered isomorphism conjecture for complex manifolds
Acta Mathematica Sinica (Impact Factor: 0.48). 09/2002; 23(4). DOI: 10.1007/s1011400507592
Source: arXiv

Article: The isomorphism conjecture for 3manifold groups and Ktheory of virtually polysurface groups
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ABSTRACT: This article has two purposes. In \cite{R3} (math.KT/0405211) we showed that the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for a particular class of 3manifolds (we denoted this class by \cal C) is the key to prove the FIC for 3manifold groups in general. And we proved the FIC for the fundamental groups of members of a subclass of \cal C. This result was obtained by showing that the double of any member of this subclass is either Seifert fibered or supports a nonpositively curved metric. In this article we prove that for any M in {\cal C} there is a closed 3manifold P such that either P is Seifert fibered or is a nonpositively curved 3manifold and \pi_1(M) is a subgroup of \pi_1(P). As a consequence this proves that the FIC is true for any Bgroup (see definition 3.2 in \cite{R3}). Therefore, the FIC is true for any Haken 3manifold group and hence for any 3manifold group (using the reduction theorem of \cite{R3}) provided we assume the Geometrization conjecture. The above result also proves the FIC for a class of 4manifold groups (see \cite{R2}(math.GT/0209119)). The second aspect of this article is to relax a condition in the definition of strongly polysurface group (\cite{R1} (math.GT/0209118)) and define a new class of groups (we call them {\it weak strongly polysurface} groups). Then using the above result we prove the FIC for any virtually weak strongly polysurface group. We also give a corrected proof of the main lemma of \cite{R1}.Journal of Ktheory Ktheory and its Applications to Algebra Geometry and Topology 08/2004; · 0.75 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: In this Paper, we investigate the effects of space noncommutativity and the generalized uncertainty principle on the stability of circular orbits of particles in a central force potential. We show that, up to first order in noncommutativity parameter, an angular momentum dependent term will be appear in the equations of the particle orbits which affects the stability of circular orbits. In the case of high angular momentum, the condition for stability of circular orbits will change considerably relative to commutative case.Chaos Solitons & Fractals 01/2008; 37(2):324331. · 1.25 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The Farrell–Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example, for discrete subgroups of Lie groups [F.T. Farrell, L.E. Jones, Isomorphism conjectures in algebraic Ktheory, J. Amer. Math. Soc. 6 (1993) 249–297], virtually polyinfinite cyclic groups [F.T. Farrell, L.E. Jones, Isomorphism conjectures in algebraic Ktheory, J. Amer. Math. Soc. 6 (1993) 249–297], Artin braid groups [F.T. Farrell, S.K. Roushon, The Whitehead groups of braid groups vanish, Internat. Math. Res. Notices 10 (2000) 515–526], a class of virtually polysurface groups [S.K. Roushon, The isomorphism conjecture for 3manifold groups and Ktheory of virtually polysurface groups, math.KT/0408243, KTheory, in press] and virtually solvable linear group [F.T. Farrell, P.A. Linnell, KTheory of solvable groups, Proc. London Math. Soc. (3) 87 (2003) 309–336]. We extend these results in the sense that if G is a group from the above classes then we prove the conjecture for the wreath product G≀H for H a finite group. The need for this kind of extension is already evident in [F.T. Farrell, S.K. Roushon, The Whitehead groups of braid groups vanish, Internat. Math. Res. Notices 10 (2000) 515–526; S.K. Roushon, The Farrell–Jones isomorphism conjecture for 3manifold groups, math.KT/0405211, KTheory, in press; S.K. Roushon, The isomorphism conjecture for 3manifold groups and Ktheory of virtually polysurface groups, math.KT/0408243, KTheory, in press]. We also prove the conjecture for some other classes of groups.Topology and its Applications. 01/2007;
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