Symmetric and Quasi-symmetric Riemann Surfaces |
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A₁ action of D(X action on H₁(X analytic manifold apply Lemma applying H(U B₁ B₂ boundary curves iff canonical homology basis Chapter Cornell University CORNELL UNIVERSITY LIBRARY Corollary 3.12 cross-caps curves iff f D₁(X denote element equivalence class equivalence relation exists h extended homogeneous symplectic fixed point set follows group of diffeomorphisms H₁ holomorphic 1-forms homogeneous symplectic group hypothesis and Lemma identify each point implies induced action induction hypothesis Jordan curve let M(X lower right hand M₁ M₂ non-orientable surface normal subgroup numbers orientable surface orientation reversing period matrices permutation matrix Proof of Theorem Proposition prove pullback quadratic form quasi-reflection QUASI-SYMMETRIC RIEMANN SURFACES quotient space r+1 boundary curves real analytic reflection resp Robert Zarrow simple calculation shows skew-symmetric surface of genus SYMMETRIC AND QUASI-SYMMETRIC symplectic modular group t₁ Theorem 3.5 thesis unimodular V₁ є Г