Linfan Mao Automorphism Groups of Maps, Surfaces and Smarandache Geometries

A combinatorial map is a connected topological graph cellularly embeddedin a surface. This monograph concentrates on the automorphism groupof a map, which is related to the automorphism groups of a Klein surfaceand a Smarandache manifold, also applied to the enumeration of unrootedmaps on orientable and non-orientable surfaces. A number of results for theautomorphism groups of maps, Klein surfaces and Smarandache manifoldsand the enumeration of unrooted maps underlying a graph on orientableand non-orientable surfaces are discovered. An elementary classification forthe closed s-manifolds is found. Open problems related the combinatorialmaps with the differential geometry, Riemann geometry and Smarandachegeometries are also presented in this monograph for the further applicationsof the combinatorial maps to the classical mathematics.