Variation of the Topological Structure of Level Surfaces |
Common terms and phrases
acquires an infinite Alexander-Pontryagin duality theorem Apk f Apk-1 f Apn-k f Betti groups Betti numbers mod Bk f Bockstein boundaried manifold circumference closed manifold components continuously differentiable function cycle homologous cycle z cycles zk deleted diagonal form direct product Èl'sgol'c Euclidean space f and decreasing f₁ factor with respect finite order func function f hence homeomorphic homologous to zero homology sphere increasing type infinite cyclic factor infinite cyclic group intersection matrix k-cycles L. S. Pontryagin lemma loses an infinite manifold M2k Morse neighborhood non-degenerate critical point obtain passes through f(p place the intersection point of decreasing points of type possible pre-critical level surface Proof relation remaining BS f Remark respect to B-1 results of L. S. set f topological product torsion groups twice continuously differentiable type k variation x passes zk M2k