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/up-in-smoke-thorax-fr-fleece-welding-hoodie-black-black-for-sale/