Exercises

2.1Prove that for any two semioriented curves with the same code (of the kind introduced in 3.7) there exists a homeomorphism of $\mathbb{R}P^2$ which maps one of them to another preserving semiorientations.

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2.2 Prove that for any two curves $A_1$, $A_2$ with the same code of their complex schemes (see Subsection 2.5) there exists a homeomorphism $\mathbb{C}A_1\cup\mathbb{R}P^2\to \mathbb{C}A_2\cup\mathbb{R}P^2$ commuting with $conj$.

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2.3 Deduce 2.7.A and 2.7.B from 2.7.C and, vise versa, 2.7.C from 2.7.A and 2.7.B.