Given a graph covering, there is an induced surjection of critical groups. We will try to determine the structure of the kernel and give results at different levels of generality. A main tool will be dualizing the short exact sequence and working instead with the cokernel. In the case of signed graphs and two-sheeted coverings, we will show that the kernel… (More)
We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade and Ram.
Graph coverings are known to induce surjections of their critical groups. Here we describe the kernels of these morphisms in terms of data parametrizing the covering. Regular coverings are parametrized by voltage graphs, and the above kernel can be identified with a naturally defined voltage graph critical group. For double covers, the voltage graph is a… (More)