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Main Authors:	Choi, Suyoung, Yoon, Younghan
Format:	Preprint
Published:	2023
Subjects:	Algebraic Topology 57S12, 14M25, 57N65, 55U10
Online Access:	https://arxiv.org/abs/2308.12693
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author	Choi, Suyoung Yoon, Younghan
author_facet	Choi, Suyoung Yoon, Younghan
contents	A permutohedral variety is a remarkable object in various areas of mathematics, and its topological invariants are widely recognized. However, only little is known about a real permutohedral variety, that is, the real locus of a permutohedral variety. The rational Betti numbers of real permutohedral varieties were computed in terms of alternating permutations in 2012. In this paper, we provide explicit descriptions of the cohomology ring of real permutohedral varieties. In particular, we describe the multiplicative structure in terms of alternating permutations.
format	Preprint
id	arxiv_https___arxiv_org_abs_2308_12693
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	The cohomology rings of real permutohedral varieties Choi, Suyoung Yoon, Younghan Algebraic Topology 57S12, 14M25, 57N65, 55U10 A permutohedral variety is a remarkable object in various areas of mathematics, and its topological invariants are widely recognized. However, only little is known about a real permutohedral variety, that is, the real locus of a permutohedral variety. The rational Betti numbers of real permutohedral varieties were computed in terms of alternating permutations in 2012. In this paper, we provide explicit descriptions of the cohomology ring of real permutohedral varieties. In particular, we describe the multiplicative structure in terms of alternating permutations.
title	The cohomology rings of real permutohedral varieties
topic	Algebraic Topology 57S12, 14M25, 57N65, 55U10
url	https://arxiv.org/abs/2308.12693

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