Can any one assist me to give me concept of Handles in the coset diagram? How do we identify it and how can we make new presentaions by joining the handles of the coset diagrams of distinct groups? Any material relating to the composition of the coset diagrams?
2026-03-28 14:26:01.1774707961
Stitching of Coset Diagrams
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Concept of Handles in Coset Diagram was first intoduced by W.W.Stothers. For instanc if we making a coset diagram of subgroup of index 14 of extended triangle group trianglegroup $ (2,3,7)=<x,y,t;x^2,y^3,t^2,(xt)^2,(yt)^2,(xy)^7> $ where x is represented by Edges y by triangle (3-gon) permuted anticlockwise and t is the reflection along the vertical axis of symmetry.
Those points in the coset diagram which are fixed by x that are represented by heavy dot and permuted in t i.e parallel to the axis of symmetry, such pairs in the coset diagram are called handle in teh coset diagrams.