On embedding all -manifolds into a single -manifold

Authors:
Fan Ding, Shicheng Wang and Jiangang Yao

Journal:
Trans. Amer. Math. Soc. **360** (2008), 6017-6030

MSC (2000):
Primary 57N35

DOI:
https://doi.org/10.1090/S0002-9947-08-04439-5

Published electronically:
June 13, 2008

MathSciNet review:
2425700

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Abstract: For each composite number , there does not exist a single connected closed -manifold such that any smooth, simply-connected, closed -manifold can be topologically flatly embedded into it. There is a single connected closed -manifold such that any simply-connected, -manifold can be topologically flatly embedded into if 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:
https://doi.org/10.1090/S0002-9947-08-04439-5

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.