Limits of (certain) CAT(0) groups, I: Compactification

Limits of (certain) Cat(0) Groups, I: Compactification

The purpose of this paper is to investigate torsion-free groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats, as defined by Hruska [18]. Our approach is to seek results analogous to those of Sela, Kharlampovich and Miasnikov for free groups and to those of Sela (and Rips and Sela) for torsion-free hyperbolic groups. This paper is the first in a series. In...

3 1 M ay 2 00 4 LIMITS OF ( CERTAIN ) CAT ( 0 ) GROUPS , I : COMPACTIFICATION

The purpose of this paper is to investigate torsionfree groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats and relatively thin triangles, as defined by Hruska [17]. Our approach is to seek results analogous to those of Sela, Kharlampovich and Miasnikov for free groups and to those of Sela (and Rips and Sela) for torsion-free hyperbolic groups. This paper...

2 00 4 Limits of ( Certain ) Cat ( 0 ) Groups , I : Compactification

The purpose of this paper is to investigate torsionfree groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats and relatively thin triangles, as defined by Hruska [17]. Our approach is to seek results analogous to those of Sela, Kharlampovich and Miasnikov for free groups and to those of Sela (and Rips and Sela) for torsion-free hyperbolic groups. This paper...

Certain Topological Groups Are Type I

The purpose of this paper is to prove a theorem which roughly states that if G is a topological group with a "sufficiently large" Type I subgroup H, then G itself is also Type I. The main tool in the proof of this theorem is a result of Tomiyama [3] which gives a sufficient condition for a subalgebra of a Type I von Neumann algebra to be Type I. As far as the author knows, this result of Tomiya...

Generalized Covering Groups and Direct Limits