arXiv subjects

S. K. Roushon

Publications and source records attributed to S. K. Roushon.

24 records · Page 2Linked to original sources

arXiv2005

The fibered isomorphism conjecture for complex manifolds

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 large 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 group of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds.

math.GT↗

arXiv2004

K-theory of virtually poly-surface groups

In this paper we generalize the notion of strongly poly-free group to a larger class of groups, we call them strongly poly-surface groups and prove that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for any virtually strongly poly-surface group. A consequence is that the Whitehead group of a torsion free subgroup of any virtually strongly poly-surface group vanishes.

math.GT↗

arXiv2004

Correction to `K-theory of virtually poly-surface groups'

In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.

math.GT↗

arXiv2004

Topology of 3-manifolds and a class of groups II

This is a continuation of an earlier preprint (math.GT/0209121) under the same title. These papers grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or trivial first homology group. With this motivation we defined a new class of groups. These groups are in some sense eventually perfect. Here we prove results giving several classes of examples of groups which do (not) belong to this class. Also we prove some basic results on these groups and state two conjectures. A direct application of one of the conjectures to the virtual Betti number conjecture is mentioned. For completeness, here we reproduce parts of math.GT/0209121.

math.GT↗

arXiv2002

Topology of 3-manifolds and a class of groups

This paper grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or trivial first homology group. With this motivation we define a new class of groups. These groups are in some sense eventually perfect. We prove results giving several classes of examples of groups which do (not) belong to this class. Also we prove some elementary results on these groups and state two conjectures. A direct application of one of the conjectures to the virtual Betti number conjecture of Thurston is mentioned.

math.GT↗

arXiv2001

A representation of generalized braid group in classical braid group

We ask if any finite type generalized braid group is a subgroup of some classical Artin braid group. We define a natural map from a given finite type generalized braid group to a classical braid group and ask if this map is an injective homomorphism. We prove that this map is a homomorphism for the braid groups of type A_n, B_n, I_2(k). The injectivity question of this homomorphism (in these particular cases) is not yet settled. If this map is an injective homomorphism then several results will follow. For example it will follow that the Whitehead group, projective class group and the lower K-group of any subgroup of any finite type generalized braid group vanish. (For the classical braid group case this vanishing result is proved by the author and F.T. Farrell in the paper "The Whitehead groups of braid groups vanish".) Also it will follow that a finite type generalized braid group satisfies Tits alternative (recently this was asked by M. Bestvina).

math.GR↗