The $p$-primary subgroups of the cohomology of $BPU_n$ in dimensions less than $2p+5$
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- by Xing Gu, Yu Zhang, Zhilei Zhang and Linan Zhong
- Proc. Amer. Math. Soc. 150 (2022), 4099-4111
- DOI: https://doi.org/10.1090/proc/16000
- Published electronically: May 27, 2022
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Abstract:
Let $PU_n$ denote the projective unitary group of rank $n$ and $BPU_n$ be its classifying space. For an odd prime $p$, we extend previous results to a complete description of $H^s(BPU_n;\mathbb {Z})_{(p)}$ for $s<2p+5$ by showing that the $p$-primary subgroups of $H^s(BPU_n;\mathbb {Z})$ are trivial for $s = 2p+3$ and $s = 2p+4$.References
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Bibliographic Information
- Xing Gu
- Affiliation: Institute for Theoretical Sciences and School of Science, Westlake University, 600 Dunyu Road, 310030, Hangzhou, Zhejiang, China; and Center for Topology and Geometry based Technology, School of Mathematical Sciences, Hebei Normal University, 20 Nanerhuandong Road, 050010, Shijiazhuang, Hebei, China
- MR Author ID: 1394209
- ORCID: 0000-0003-0866-8403
- Email: guxing@westlake.edu.cn
- Yu Zhang
- Affiliation: Department of Mathematics, Nankai University, 94 Weijin Road, Nankai District, 300071, Tianjin, People’s Republic of China
- ORCID: 0000-0001-9751-3360
- Email: Zhang.4841@osu.edu
- Zhilei Zhang
- Affiliation: Department of Mathematics, Nankai University, 94 Weijin Road, Nankai District, 300071, Tianjin, People’s Republic of China
- Email: 15829207515@163.com
- Linan Zhong
- Affiliation: Department of Mathematics, Yanbian University, No. 997 Gongyuan Road, 133000, Yanji, Jilin Province, People’s Republic of China
- Email: lnzhong@ybu.edu.cn
- Received by editor(s): August 21, 2021
- Received by editor(s) in revised form: December 6, 2021, and December 7, 2021
- Published electronically: May 27, 2022
- Additional Notes: The first author was supported by the National Natural Science Foundation of China (No. 21113062) and the High-level Scientific Research Foundation of Hebei Province (No. 13113093). The second author and the third author were supported by the National Natural Science Foundation of China (No. 11871284). The fourth author was supported by the National Natural Science Foundation of China (No. 12001474; 11761072).
All authors contributed equally. The fourth author is the corresponding author. - Communicated by: Julie Bergner
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4099-4111
- MSC (2020): Primary 55T10, 55R35, 55R40
- DOI: https://doi.org/10.1090/proc/16000
- MathSciNet review: 4446254