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Contents
Analytic and Algebraic Topology | 1 |
Problems and Examples པ | 5 |
Part I | 13 |
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2-sphere algebraic algebraic topology arbitrary assertion barystar basic cycle basis elements Betti numbers boundary operator called canonical bases carrier simplex cell decomposition chain complex chain mapping cochain cocycle cohomology classes complementary cells completes the proof connected continuous mapping corresponding Cp+q Cq(K Cq+1 cup product defined definition deformation deformation retract denote dimension q elementary cochains epimorphic equation following theorem groups and cohomology Ha(K Hence homo homology groups homology theory homomorphism homotopy type Hq(K Hq(R identity mapping induced integer invariant isomorphic K₁ Kronecker product manifold Mn mapping f matrix modules morphism n-dimensional chain n-dimensional manifold n-simplexes normal subdivision oriented simplexes polyhedra polyhedron Pp+q pseudomanifold retract simplicial approximation simplicial complex simplicial decomposition simplicial mapping solid sphere space stars St subcomplex summands Theorem topology torsion uniquely determined valid vertex stars vertices zero