  We discuss the extension of loop quantum gravity to topspin networks, a
proposal which allows topological information to be encoded in spin networks.
We will show that this requires minimal changes to the phase space, C*-algebra
and Hilbert space of cylindrical functions. We will also discuss the area and
Hamiltonian operators, and show how they depend on the topology. This extends
the idea of "background independence" in loop quantum gravity to include
topology as well as geometry. It is hoped this work will confirm the usefulness
of the topspin network formalism and open up several new avenues for research
into quantum gravity.
