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Forum Mathematicum

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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
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Published Online: 2016-08-30 | DOI: https://doi.org/10.1515/forum-2016-0025


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.

Keywords: Real toric manifold; small cover; real topological toric manifold; cohomology ring; odd torsion; nestohedron

MSC 2010: 57N65; 57S17; 05E45


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About the article

Received: 2016-01-29

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, DOI: https://doi.org/10.1515/forum-2016-0025.

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