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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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1435-5337
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Volume 29, Issue 3

# On the cohomology and their torsion of real toric objects

Suyoung Choi
/ Hanchul Park
• Corresponding author
• School of Mathematics, Korea Institute for Advanced Study (KIAS), 85 Hoegiro Dongdaemun-gu, Seoul 130-722, Republic of Korea
• Email
• Other articles by this author:
Published Online: 2016-08-30 | DOI: https://doi.org/10.1515/forum-2016-0025

## Abstract

In this paper, we do the following two things:

• (i)

We present a formula to compute the rational cohomology ring of a real topological toric manifold, and thus that of a small cover or a real toric manifold, which implies the formula of Suciu and Trevisan. Furthermore, the formula also works for an arbitrary coefficient ring G in which 2 is a unit.

• (ii)

We construct infinitely many real toric manifolds and small covers whose integral cohomology rings have a q-torsion for any positive odd integer q.

MSC 2010: 57N65; 57S17; 05E45

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Revised: 2016-07-01

Published Online: 2016-08-30

Published in Print: 2017-05-01

Funding Source: National Research Foundation of Korea

Award identifier / Grant number: NRF-2012R1A1A2044990

This research was supported by the Basic Science Research Program of the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2012R1A1A2044990).

Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 543–553, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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## Citing Articles

[1]
Suyoung Choi, Shizuo Kaji, and Hanchul Park
Proceedings of the Edinburgh Mathematical Society, 2019, Volume 62, Number 3, Page 861
[2]
Hanchul Park
Chinese Annals of Mathematics, Series B, 2017, Volume 38, Number 6, Page 1321
[3]
Suyoung Choi, Boram Park, and Hanchul Park
Chinese Annals of Mathematics, Series B, 2017, Volume 38, Number 6, Page 1213
[4]
Jiming Ma and Fangting Zheng
Chinese Annals of Mathematics, Series B, 2017, Volume 38, Number 6, Page 1311