Open Access
Jan. 2002 Retracting compact 3-manifolds onto their boundary components
Ensil Kang
Proc. Japan Acad. Ser. A Math. Sci. 78(1): 10-13 (Jan. 2002). DOI: 10.3792/pjaa.78.10


Let $X$ be a compact 3-manifold and $A$ a boundary component of $X$ to which $X$ retracts. We propose the problem of classifying such $(X,A)$ up to PL homeomorphisms in a suitable class of manifolds. We give a complete solution in a special case. We show in this case there are exactly twenty-four basic pairs $(X,A)$ and all other cases are obtained from these by some obvious modifications. If $A$ is assumed to be different from a 2-sphere, there are six basic pairs.


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Ensil Kang. "Retracting compact 3-manifolds onto their boundary components." Proc. Japan Acad. Ser. A Math. Sci. 78 (1) 10 - 13, Jan. 2002.


Published: Jan. 2002
First available in Project Euclid: 23 May 2006

zbMATH: 0998.57042
MathSciNet: MR1879856
Digital Object Identifier: 10.3792/pjaa.78.10

Primary: 57M50 , 57N16
Secondary: 57M60

Keywords: 3-manifold , retraction

Rights: Copyright © 2002 The Japan Academy

Vol.78 • No. 1 • Jan. 2002
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