On embedding all $n$-manifolds into a single $(n+1)$-manifold
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- by Fan Ding, Shicheng Wang and Jiangang Yao PDF
- Trans. Amer. Math. Soc. 360 (2008), 6017-6030 Request permission
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.References
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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
- 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 [Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269–331 (1978)]
The first two authors were partially supported by grant No. 10201003 of NSFC and a grant of MSTC - © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 360 (2008), 6017-6030
- MSC (2000): Primary 57N35
- DOI: https://doi.org/10.1090/S0002-9947-08-04439-5
- MathSciNet review: 2425700