Abstract In this paper we propose a Hamiltonian approach to gapped topological phases on open surfaces. Our setting is an extension of the Levin-Wen model to a 2d graph on an open surface. whose boundary is part of the graph. We systematically construct a series of boundary Hamiltonians such that each of them. https://www.pomyslnaszycie.com/us-topo-7-5-minute-map-for-booger-canyon-az-fashion/