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Different types of cut corners

Different types of cut corners

Source publication
Figure 2: An illustration of thin map
Figure 3: Gluing two regions
Figure 4: Different types of cut corners
Figure 5: Making a diagram a proper V (6) diagram
+1 Figure 6: Replacing edge labeled by x p i with edge labeled by x m ii −p i
On Shephard Groups with Large Triangles
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  • Dec 2008
Shephard groups are common extensions of Artin and Coxeter groups. They appear, for example, in algebraic study of manifolds. An infinite family of Shephard groups which are not Artin or Coxeter groups is considered. Using techniques form small cancellation theory we show that the groups in this family are bi-automatic. Comment: 30 pages, 11 PDF fi...
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Contexts in source publication

Context 1
... we mainly work with derived diagrams we also describe afterward how to use this property in our context. See Figure 4 for illustrations of cases 1 through 4. Next theorem link between cut corners, thin maps, and proper V (6) maps. It is one of the main ingredients in the proof of Proposition 13. ...
Context 2
... In this step we treat the case that (r, s) = (2, 2). Here, ∆ is a cut corner of type T2 (see Figure 4 -case 2). We have that m ij = 2 and that the number of syllables in ∂∆ is exactly four (it is at least four by the Apple-Schupp syllable length condition and it is at most four by the assumption at the end of step 2). ...
Context 3
... we get that = j. There are two sub-cases to consider, the case where ∆ is a cut corner of type T 3 and the case of type T 4 (see Figure 4 -cases 3 and 4). ...

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