内容简介

Since the first monograph titled Enumerative Theory of Maps appeared on the subject considered in 1999, many advances have been made by the author himself and those directed by him under such a theoretical foundation.
Because of that book with much attention to maps on surface of genus zero, this monograph is in principle concerned with maps on surfaces of genus not zero. Via main theoretical lines, this book is divided into four parts except Chapter 1 for preliminaries.
Part one contains Chapters 2 through 10. The theory is presented for maps on general surfaces of genus not necessary to be zero. For the theory on a surface of genus zero is comprehensively improved for investigating maps on all surfaces of genera not zero.
Part two consists of only Chapter 11. Relationships are established for building up a bridge between super maps and embeddings of a graph via their automorphism groups.
Part three consists of Chapters 12 and 13. A general theory for finding genus distribution of graph embeddings, handle polynomials and crosscap polynomials of super maps are constructed on the basis of the joint tree method which enables us to transform a problem in a high dimensional space into a problem on a polygon.
All other chapters, i.e., Chapters 14 through 17, as part four are concerned with several aspects of main extensions to distinct directions.
An appendix serves as atlas of super maps of typical graphs of small size on surfaces for the convenience of readers to check their understanding.