  We construct a new polynomial invariant of maps (graphs embedded in a compact
surface, orientable or non-orientable), which contains as specializations the
Krushkal polynomial, the Bollob\'as--Riordan polynomial, the Las Vergnas
polynomial, and their extensions to non-orientable surfaces, and hence in
particular the Tutte polynomial. Other evaluations include the number of local
flows and local tensions taking non-identity values in a given finite group.
