A discrete Homotopy Theory for Graphs and its Relation to Subspace ArrangementsAlgebra & Discrete Mathematics
|Helene Barcelo, Arizona State University
|Fri, Nov 19 2004, 12:10PM
We present the construction of a bigraded family of groups (A-groups) associated to graphs, and simplicial complexes. This theory resembles classical homotopy theory of spaces and satisfies many of the same properties. However, it depends heavily on the combinatorial structure of the objects; for instance, it is not invariant under subdivisions of simplicial complexes. We will discuss the connections between the A-groups associated to the order complex of the Boolean lattice and the classical homotopy groups of the complement of the k-equal arrangements.