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CHAPTER ONE TwoDimensional Manifolds
Definition and examples of nmanifolds
Orientable vs nonorientable manifolds
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algebraic topology arcwise connected assume automorphism base point bordered surface boundary Chapter Choose circle closed path compact surface component connected sum consider contained continuous map Corollary coset countable CW-complex defined definition deformation retract denote disc edge path element elementary neighborhood epimorphism equivalence class Euclidean Euler characteristic example Exercise exists a unique Figure finite number free abelian group free group free product fundamental group group G group ir(X Hausdorff space Hence homeomorphic homology homotopy type inclusion map initial point integer ir(A ir(M ir(U ir(Y isomorphic Lemma Let F let G manifold maps f maximal tree noncompact nonorientable normal subgroup notation open sets open subset orientable pairs path class point x0 polygon projective plane Proposition prove quotient group quotient space quotient topology reader regular covering space Section Seifert-Van Kampen theorem simply connected subcomplex subgroup of G subspace terminal point Theorem 5.1 topological space torus triangulation vertex vertices