# Ascending HNN extensions and the BNS invariant

12 June 2013
16:00
Benno Kuckuck
Abstract
<p><span><span style="color: black; font-family: Calibri; font-size: small;"><span style="font-size: 12pt;"> <div></div> <div>&nbsp;To any splitting of a group G as an HNN extension we can associate a map from G to Z. Conversely, a group that allows a non-trivial homomorphism to Z may be written as an HNN extension in an obvious way. In this talk we will consider the question when such a homomorphism G-&gt;Z is associated to a non-obvious HNN splitting of G. We will then see how this information can be collected into an invariant of the group which may be described by a simple connectivity condition on Cayley graphs.<span><span style="color: black; font-family: Calibri; font-size: small;"><span style="font-size: 12pt;"> </span></span></span></div> </span></span></span></p>
• Junior Topology and Group Theory Seminar