Poset Path Splitting

Matteus Froese, University of Waterloo

In 2001, Hoffman introduced an analogue of a covering space for a ranked, locally finite poset. The author proved an existence and uniqueness theorem for universal covers in this framework and explored a number of examples. We extend this work to the case of finite, but not necessarily ranked, posets. We give a characterization of the covering spaces in terms of paths of the original poset. We use this characterization to show that the set of all covering spaces naturally forms a supersolvable lattice and explore some of its properties. In particular, we classify when it is semidistributive and extremal. Finally, we give an analogue of a deck transformation and show that the automorphism group of a poset is intimately related to the automorphism group of its covering space lattice. This is joint work with Ian George.