In a joint paper with M. Mihalik, a theorem of the following type was proved: If G is a one-ended group acting geometrically on a CAT(0) space X and it is known that G splits as an amalgamated product in a “special way” (to be

described in the talk), then the visual boundary of X is connected but not locally connected. In joint work in progress with C. Hruska, we consider a full converse to this theorem in the setting of groups acting on CAT(0) spaces with

the Isolated Flats Property. In this talk, we will discuss several motivating examples in detail. The groups in question here are known to be relatively hyperbolic with respect to the stabilizers of flats, thus one can also consider the Bowditch boundary of such a group. We discuss the relationship between the visual boundary of the space X and the Bowditch boundary of the group G; this is crucial in our approach to the converse of the splitting theorem.

# A converse to a splitting theorem

Event time:

Thursday, February 17, 2005 - 11:30am to Wednesday, February 16, 2005 - 7:00pm

Location:

431 DL

Speaker:

Kim Ruane

Speaker affiliation:

Tufts

Event description: