Thomas Koberda
On some of the residual properties of finitely generated nilpotent groups.
Thu, 02/18/2010 - 16:01 — SomNambulAuthors: Thomas Koberda
Subjects: Group Theory
AbstractIn this note we will also show that a nonabelian nilpotent group is either
virtually abelian or is not virtually RFRS, a result which may be of
independent interest though not directly applicable to 3-manifold topology.
This result also illustrates some of the interplay between residual
torsion-free nilpotence and the RFRS condition, especially in the context of
graph groups. Residual properties of graph groups have been of great interest
recently, in part because of the work of many authors on the virtually fibered
conjecture.Residual properties of certain 3-manifold groups.
Tue, 10/13/2009 - 18:46 — SomNambulAuthors: Thomas Koberda
Subjects: Geometric Topology
AbstractLet $M=M^3$ be a fibered 3-manifold. It is well-known that $G=\pi_1(M)$ is
residually solvable and even residually finite solvable. In this note we
understand when $G$ is residually nilpotent, having observed that $G$ is always
virtually residually nilpotent. We then prove that 3-manifold groups which are
constructed from virtually fibered 3-manifolds have, for every prime $p$,
virtually residually finite $p$ fundamental groups.Residual properties of certain 3-manifold groups.
Tue, 10/13/2009 - 18:46 — SomNambulAuthors: Thomas Koberda
Subjects: Geometric Topology
AbstractLet $M=M^3$ be a fibered 3-manifold. It is well-known that $G=\pi_1(M)$ is
residually solvable and even residually finite solvable. In this note we
understand when $G$ is residually nilpotent, having observed that $G$ is always
virtually residually nilpotent. We then prove that 3-manifold groups which are
constructed from virtually fibered 3-manifolds have, for every prime $p$,
virtually residually finite $p$ fundamental groups.Asymptotic homological linearity of the mapping class group and a homological version of the Nielsen-Thurston classification.
Fri, 10/02/2009 - 09:41 — SomNambulAuthors: Thomas Koberda
Subjects: Geometric Topology
AbstractWe study the action of the mapping class group with one marked point on the
rational homology of finite nilpotent covers of a hyperbolic Riemann surface.
We use the homological representation of the mapping class to construct a
faithful infinite-dimensional representation of the mapping class group. We
show that this representation detects the Nielsen-Thurston classification of
each mapping class. We then discuss some examples that occur in the theory of
braid groups. Finally, we discuss an analogous theory for automorphisms of free
groups.Asymptotic homological linearity of the mapping class group and a homological version of the Nielsen-Thurston classification.
Fri, 10/02/2009 - 09:41 — SomNambulAuthors: Thomas Koberda
Subjects: Geometric Topology
AbstractWe study the action of the mapping class group with one marked point on the
rational homology of finite nilpotent covers of a hyperbolic Riemann surface.
We use the homological representation of the mapping class to construct a
faithful infinite-dimensional representation of the mapping class group. We
show that this representation detects the Nielsen-Thurston classification of
each mapping class. We then discuss some examples that occur in the theory of
braid groups. Finally, we discuss an analogous theory for automorphisms of free
groups.
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