On the Dehn Complex of Virtual Links
A virtual link comes with a variety of link complements. This paper is concerned with the Dehn space, a pseudo-manifold with boundary, and the Dehn complex, a two-dimensional spine of the Dehn space. In the classical case where the link is planar, the Dehn space is the link complement in the 3-sphere. We study topological and geometric properties of the Dehn complex of a virtual link. Among other things, we show that every finitely presented group is the fundamental group of a Dehn complex, and that the Dehn complex of any alternating triple of an alternating virtual link is a non-positively curved squared complex.
Byrd, Rachel and Harlander, Jens. (2013). "On the Dehn Complex of Virtual Links". Journal of Knot Theory and Its Ramifications, 22(7), 1350033-1 - 1350033-13.