Automorphism groups of compact bordered Klein surfaces

Automorphism groups of compact bordered Klein surfaces

by Emilio Bujalance, Jose J. Etayo, Jose Manuel Gamboa, G. Gromadzki

Part of Lecture notes in mathematics ;

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This research monograph provides a self-contained approach to the problem of determining the conditions under which a compact bordered Klein surface S and a finite group G exist, such that G acts as a group of automorphisms in S. The cases dealt with here take G cyclic, abelian, nilpotent or supersoluble and S hyperelliptic or with connected boundary. No advanced knowledge of group theory or hyperbolic geometry is required and three introductory chapters provide as much background as necessary on non-euclidean crystallographic groups. The graduate reader thus finds here an easy access to current research in this area as well as several new results obtained by means of the same unified approach.

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    How did the authors' systematic approach to non-euclidean crystallographic groups shape your understanding of mathematical symmetry, and can you recall a moment in your own life when a complex, chaotic problem suddenly revealed an underlying, elegant structure?

  2. 2

    In what ways does the restriction of the group G to cyclic, abelian, nilpotent, or supersoluble structures reflect broader human tendencies to categorize the infinite, and how do you personally balance the desire for order with the reality of complex systems?

  3. 3

    The monograph builds its foundation through three introductory chapters before diving into advanced research; how did preparing for this intellectual journey mirror a time in your life when you had to master unfamiliar fundamentals before tackling a daunting project?

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