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This is shown in MR1310882

MR1310882 (95m:05091) 
Negami, Seiya  (J-YOKOED) 
Diagonal flips in triangulations of surfaces. (English summary) 
Discrete Math. 135 (1994), no. 1-3, 225–232. You

You can check it out.check it out. You will note that the argument uses some heavy lifting, unlike Hatcher's.

This is shown in MR1310882 (95m:05091) Negami, Seiya(J-YOKOED) Diagonal flips in triangulations of surfaces. (English summary) Discrete Math. 135 (1994), no. 1-3, 225–232. You can check it out. You will note that the argument uses some heavy lifting, unlike Hatcher's.

This is shown in

MR1310882 (95m:05091) 
Negami, Seiya  (J-YOKOED) 
Diagonal flips in triangulations of surfaces. (English summary) 
Discrete Math. 135 (1994), no. 1-3, 225–232.

You can check it out. You will note that the argument uses some heavy lifting, unlike Hatcher's.

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Igor Rivin
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This is shown in MR1310882 (95m:05091) Negami, Seiya(J-YOKOED) Diagonal flips in triangulations of surfaces. (English summary) Discrete Math. 135 (1994), no. 1-3, 225–232. You can check it out. You will note that the argument uses some heavy lifting, unlike Hatcher's.