Hypermap operations of finite order

2009/11/13 by Jones, Gareth A., Pinto, Daniel
#05C10 #05C25 #20F28 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.0911.2644

Abstract

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 Δ≅ PGL₂(\bf Z) and \rm Out Δ⁺≅ GL₂(\bf Z) of the groups Δ= C₂*C₂*C₂ and Δ⁺ = F₂. We will consider the elements of finite order in these two groups, and the operations they induce.

Related

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• Chirality Groups of Maps and Hypermaps
• Hypermaps and multiply quasiplatonic Riemann surfaces
• Chiral covers of hypermaps
• Duality on hypermaps with symmetric or alternating monodromy group