Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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USING ROTATIONALLY SYMMETRIC PLANES TO ESTABLISH TOPOLOGICAL FINITENESS OF MANIFOLDS

  • Eric Choi (Department of Mathematics and Statistics Georgia Gwinnett College)
  • Received : 2023.04.04
  • Accepted : 2023.10.19
  • Published : 2024.03.31
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Abstract

Let (M, p) denote a noncompact manifold M together with arbitrary basepoint p. In [7], Kondo-Tanaka show that (M, p) can be compared with a rotationally symmetric plane Mm in such a way that if Mm satisfies certain conditions, then M is proved to be topologically finite. We substitute Kondo-Tanaka's condition of finite total curvature of Mm with a weaker condition and show that the same conclusion can be drawn. We also use our results to show that when Mm satisfies certain conditions, then M is homeomorphic to ℝn.

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References

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