"""The actual successive attachment maps of CG-S6-06. CC0-1.0.""" from pathlib import Path from xml.sax.saxutils import escape root=Path(__file__).resolve().parents[1] p=['', 'The complete fundamental group through the actual attachments', 'The middle group is the lattice semidirect a free group. The cusp kills its two torus cycles and its meridian; their normal closure leaves two commuting generators. The first finite filling imposes x cubed equals c; the second imposes x fourth equals x cubed, giving the trivial group.', '', ''] def text(x,y,s,size=23): p.append(f'{escape(s)}') def box(y,h): p.append(f'') def arrow(y1,y2): p.append(f'') text(310,37,'The full group through each attachment',28) box(62,129) text(310,98,'Middle family J',27) text(310,137,'Λ ⋊ F(ρ₁, ρ₂)',29) text(310,173,'ρⱼ t(λ) ρⱼ⁻¹ = t(Aⱼλ)',23) text(310,230,'Attach the cusp N₀',25) text(310,265,'Kill t(ŵ), t(δ̂) and a₀; ρ₁ρ₂a₀ = 1.',22) text(310,300,'A₁ŵ = û − ŵ forces û into the normal closure.',21) arrow(315,345) box(357,113) text(310,394,'ℤ² generated by c and x',28) text(310,431,'c = t(γ̂) is central; x = ρ₁, y = ρ₂ = x⁻¹.',21) text(310,510,'Attach the order-three filling N₁',25) text(310,546,'ρ₁³ = t(v₁), with γ(v₁) = +1: x³ = c.',22) arrow(560,590) box(602,91) text(310,640,'ℤ generated by x',28) text(310,675,'The relation replaces c by x³.',22) text(310,733,'Attach the order-four filling N₂',25) text(310,769,'ρ₂⁴ = t(v₂), with γ(v₂) = −1: y⁴ = c⁻¹.',21) text(310,804,'Since y = x⁻¹, x⁴ = c = x³.',23) arrow(817,848) box(860,89) text(310,896,'x = 1, c = 1, y = 1',28) text(310,933,'π₁(X) = 1',30) text(310,991,'All maps come from the specified based overlaps.',22) p.append('') (root/'assets/fundamental-group-attachments.svg').write_text('\n'.join(p)+'\n',encoding='utf-8')