## On the various notions of Poincaré duality pair

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- by John R. Klein, Lizhen Qin and Yang Su PDF
- Trans. Amer. Math. Soc.
**375**(2022), 4251-4283 Request permission

## Abstract:

We establish a number of foundational results on Poincaré spaces which result in several applications. One application settles an old conjecture of C.T.C. Wall in the affirmative. Another result shows that for any natural number $n$, there exists a finite CW pair $(X,Y)$ satisfying relative Poincaré duality in dimension $n$ with the property that $Y$ fails to satisfy Poincaré duality. We also prove a relative version of a result of Gottlieb about Poincaré duality and fibrations.## References

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## Additional Information

**John R. Klein**- Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202
- MR Author ID: 308817
- Email: klein@math.wayne.edu
**Lizhen Qin**- Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiangsu 210093, People’s Republic of China
- Email: qinlz@nju.edu.cn
**Yang Su**- Affiliation: HLM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China
- Email: suyang@math.ac.cn
- Received by editor(s): December 1, 2019
- Received by editor(s) in revised form: October 8, 2021
- Published electronically: March 31, 2022
- Additional Notes: The first author was partially supported by Simons Foundation Collaboration Grant 317496. The second author was partially supported by NSFC11871272. The third author was partially supported by NSFC11571343
- © Copyright 2022 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**375**(2022), 4251-4283 - MSC (2020): Primary 57P10; Secondary 55N25, 55N45
- DOI: https://doi.org/10.1090/tran/8630
- MathSciNet review: 4419058