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The torsion of real toric manifolds


Author: Jin Hong Kim
Journal: Proc. Amer. Math. Soc. 148 (2020), 901-911
MSC (2010): Primary 55R20, 57R65
DOI: https://doi.org/10.1090/proc/14755
Published electronically: September 20, 2019
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Abstract: In view of various results and the nature of their constructions for real toric objects, it is an interesting and also natural problem to know how much torsion can be contained in their cohomology groups. The aim of this paper is to answer this question by explicitly constructing examples of real toric objects to show the richness of torsion which can appear in the cohomology groups with coefficients in a locally constant presheaf. That is, we show that a real quasitoric manifold (or small cover) which plays an important role in the category of real toric objects can have an arbitrary amount of torsion in its cohomology groups with coefficients in a locally constant presheaf. This will be achieved by crucially using the Torsion Theorem for links of Bosio and Meersseman.


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Additional Information

Jin Hong Kim
Affiliation: Department of Mathematics Education, Chosun University, 309 Pilmun-daero, Dong-gu, Gwangju 61452, Republic of Korea
Email: jinhkim11@gmail.com

DOI: https://doi.org/10.1090/proc/14755
Received by editor(s): October 31, 2018
Received by editor(s) in revised form: January 18, 2019, and June 14, 2019
Published electronically: September 20, 2019
Additional Notes: This study was supported by a research fund from Chosun University, 2018
Communicated by: Mark Behrens
Article copyright: © Copyright 2019 American Mathematical Society