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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On embedding all $ n$-manifolds into a single $ (n+1)$-manifold


Authors: Fan Ding, Shicheng Wang and Jiangang Yao
Journal: Trans. Amer. Math. Soc. 360 (2008), 6017-6030
MSC (2000): Primary 57N35
Published electronically: June 13, 2008
MathSciNet review: 2425700
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Abstract: For each composite number $ n\ne 2^k$, there does not exist a single connected closed $ (n+1)$-manifold such that any smooth, simply-connected, closed $ n$-manifold can be topologically flatly embedded into it. There is a single connected closed $ 5$-manifold $ W$ such that any simply-connected, $ 4$-manifold $ M$ can be topologically flatly embedded into $ W$ if $ M$ is either closed and indefinite, or compact and with non-empty boundary.


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Additional Information

Fan Ding
Affiliation: LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: dingfan@math.pku.edu.cn

Shicheng Wang
Affiliation: LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: wangsc@math.pku.edu.cn

Jiangang Yao
Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94720
Email: jgyao@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04439-5
PII: S 0002-9947(08)04439-5
Received by editor(s): September 1, 2005
Received by editor(s) in revised form: May 12, 2006, and October 31, 2006
Published electronically: June 13, 2008
Additional Notes: The authors would like to thank Jianzhong Pan for informing them of Sullivan’s work \cite{Su}
The first two authors were partially supported by grant No. 10201003 of NSFC and a grant of MSTC
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.