Algebraic Topology: An Introduction |
Contents
CHAPTER ONE TwoDimensional Manifolds | 1 |
Definition and examples of nmanifolds | 2 |
Orientable vs nonorientable manifolds | 3 |
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arcwise connected assume automorphism base point bordered surface boundary Chapter Choose circle closed path compact surface component connected sum contained continuous map Corollary coset countable CW-complex defined definition deformation retract denote diagram disc disjoint edge path element elementary neighborhood epimorphism equivalence class Euler characteristic example Exercise exists a unique finite number free abelian group free group free product fundamental group G-space G₁ group G Hausdorff space Hence homeomorphic homology inclusion map initial point integer isomorphic Lemma Let F Let G manifold map f maximal tree normal subgroup open sets orientable p₁ pair path class path f projective plane proof Proposition prove quotient space quotient topology reader regular covering space Section Seifert-Van Kampen theorem semilocally simply connected subcomplex subgroup of G subspace terminal point Theorem 5.1 theory topological space torus triangulation v₁ vertex vertices x₁