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SOME OLD TOPOLOGICAL PROBLEMS
THE GEOMETRY OF COMPLEXES
THE CLASSIFICATION OF SURFACES
10 other sections not shown
abstract simplicial complex algebraic topology arbitrary assume Betti numbers bordered surfaces boundary Brou Brouwer called cell complex chain maps Claim clearly coefficients compute connected sum constant map continuous map corollary curve DEFINITION deg f denote dimension disk edges equation Euler characteristic Euler's theorem example fact FIGURE finite fixed points follows function geometric given group G homeomorphic homology groups homology theory imbedded induction inessential integer intuitive isomorphism K,cp knot labeled complex labeled polygon Lemma Let f manifolds map f Math n-dimensional n-simplices nonzero orientable surface oriented q-simplex pair path Poin Poincare polyhedra polyhedron Problem proof of Lemma proof of Theorem proved pseudomanifold q q q q-th simplex simplicial approximation simplicial complex simplicial map sphere st(v subcomplex subgroup subset Suppose symbol Theorem 15 topological invariance torsion coefficients torus triangulation Uber underlying space unique vector field vertex vertices zero