Hypermap operations of finite order

Details Hypermap operations of finite order Hypermap operations of finite order

2009-11-13

arxiv.org/abs/0911.2644v1

Mathematics

Combinatorics

14 pages. To appear in Discrete Mathematics (Proc. Bled Combinatorics Conf. 2007)

Scientific paper

Duality and chirality are examples of operations of order 2 on hypermaps. James showed that the groups of all operations on hypermaps and on oriented hypermaps can be identified with the outer automorphism groups ${\rm Out} \Delta\cong PGL_2({\bf Z})$ and ${\rm Out} \Delta^+\cong GL_2({\bf Z})$ of the groups $\Delta = C_2*C_2*C_2$ and $\Delta^+ = F_2$. We will consider the elements of finite order in these two groups, and the operations they induce.

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