## A finite quotient of join in Alexandrov geometry

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- by Xiaochun Rong and Yusheng Wang PDF
- Trans. Amer. Math. Soc.
**374**(2021), 1095-1124 Request permission

## Abstract:

Given two $n_i$-dimensional Alexandrov spaces $X_i$ of curvature $\ge 1$, the join of $X_1$ and $X_2$ is an $(n_1+n_2+1)$-dimensional Alexandrov space $X$ of curvature $\ge 1$, which contains $X_i$ as convex subsets such that their points are $\frac \pi 2$ apart. If a group acts isometrically on a join that preserves $X_i$, then the orbit space is called a quotient of join. We show that an $n$-dimensional Alexandrov space $X$ with curvature $\ge 1$ is isometric to a finite quotient of join, if $X$ contains two compact convex subsets $X_i$ without boundary such that $X_1$ and $X_2$ are at least $\frac \pi 2$ apart and $\dim (X_1)+\dim (X_2)=n-1$.## References

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## Additional Information

**Xiaochun Rong**- Affiliation: Department of Mathematics, Capital Normal University, Beijing, People’s Republic of China; and Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903
- MR Author ID: 336377
- Email: rong@math.rutgers.edu
**Yusheng Wang**- Affiliation: School of Mathematical Sciences (and Lab. math. Com. Sys.), Beijing Normal University, Beijing, 100875 People’s Republic of China
- Email: wyusheng@bnu.edu.cn
- Received by editor(s): November 17, 2018
- Received by editor(s) in revised form: May 5, 2020
- Published electronically: November 18, 2020
- Additional Notes: The first author was supported in part by NSFC 11821101, BNSF Z19003, and a research fund from Capital Normal University

The second author was supported in part by NFSC 11971057 and BNSF Z190003.

Yusheng Wang is the corresponding author - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**374**(2021), 1095-1124 - MSC (2020): Primary 53C20, 53C23, 53C24
- DOI: https://doi.org/10.1090/tran/8194
- MathSciNet review: 4196388