Using rotationally symmetric planes to establish topological finiteness of manifolds

Let $(M, p)$ denote a noncompact manifold $M$ together with arbitrary basepoint $p$. In \cite{KonTan-II}, Kondo-Tanaka show that $(M, p)$ can be compared with a rotationally symmetric plane $M_m$ in such a way that if $M_m$ satisfies certain conditions, then $M$ is proved to be topologically finite....

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2024, 61(2), , pp.511-517
Main Author: Eric Choi
Format: Article
Language:English
Subjects:
수학
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Summary:Let $(M, p)$ denote a noncompact manifold $M$ together with arbitrary basepoint $p$. In \cite{KonTan-II}, Kondo-Tanaka show that $(M, p)$ can be compared with a rotationally symmetric plane $M_m$ in such a way that if $M_m$ satisfies certain conditions, then $M$ is proved to be topologically finite. We substitute Kondo-Tanaka's condition of finite total curvature of $M_m$ with a weaker condition and show that the same conclusion can be drawn. We also use our results to show that when $M_m$ satisfies certain conditions, then $M$ is homeomorphic to $\mathbb{R}^n$. KCI Citation Count: 0
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b230203