Topology and related seminars: Daniel Wise

The "nonpositive immersion" property is a condition on a 2-complex X that generalizes being a surface. When X has this property, its fundamental group appears to have has some very nice properties which I will discuss. I will spend the remainder of the talk outlining a proof that the nonpositive immersion property holds for a 2-complex obtained by attaching a single 2-cell to a graph. This was proven recently with Joseph Helfer and also independently by Lars Louder and Henry Wilton.