arXiv subjects
Publications and source records attributed to James Dover.
We prove Csorba's conjecture that the Lovász complex Hom(C_5,K_n) of graph multimorphisms from the 5-cycle C_5 to the complete graph K_n is Z/2Z-equivariantly homeomorphic to the Stiefel manifold, V(n-1,2), the space of (ordered) orthonormal 2-frames in R^{n-1}. The equivariant piecewise-linear topology that we need is developed along the way.
For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces come up naturally in topological robotics. In this paper, we study the homotopy, homeomorphism, and isotopy types of these spaces over the space of parameters r and provide a polynomial upper bound (in the number of edges of Gamma) for the number of isotopy types.