Closed quantum surfaces from the Toeplitz extension

Closed quantum surfaces of any genus are defined as subalgebras of the Toeplitz algebra by mimicking the classical construction of identifying arcs on the boundary of the (quantum) unit disk. Isomorphism classes obtained from different arrangements of arcs are classified. It is shown that the K-groups are isomorphic to the classical counterparts and explicit generators of the C*-algebras and of the K-groups are given.