대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권2호
  • /
  • Pages.511-517
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  • 2024
  • /
  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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USING ROTATIONALLY SYMMETRIC PLANES TO ESTABLISH TOPOLOGICAL FINITENESS OF MANIFOLDS

  • Eric Choi (Department of Mathematics and Statistics Georgia Gwinnett College)
  • 투고 : 2023.04.04
  • 심사 : 2023.10.19
  • 발행 : 2024.03.31
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초록

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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참고문헌

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