Nonpositive immersions and counting cycles
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.