Cohomology of type B $B$ real permutohedral varieties

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-06-24 DOI:10.1112/blms.70125

Younghan Yoon

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Abstract

Type $A$ and type $B$ permutohedral varieties are classic examples of mathematics, and their topological invariants are well-known. This naturally leads to the investigation of the topology of their real loci, known as type $A$ and type $B$ real permutohedral varieties. The rational cohomology rings of type $A$ real permutohedral varieties are fully described in terms of alternating permutations. Until now, only rational Betti numbers of type $B$ real permutohedral varieties have been described in terms of $B$ -snakes. In this paper, we explicitly describe the multiplicative structure of the cohomology rings of type $B$ real permutohedral varieties in terms of $B$ -snakes.

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B$实复面体型变异的上同性

类型A$和类型B$是数学中的经典例子，它们的拓扑不变量是众所周知的。这自然导致了对其实位点拓扑结构的研究，称为A型A型和B型B型实多面体变异。用交替置换的方法充分描述了A$ A$实置换面体型的有理上同环。到目前为止，只有B$ B$实多面体型的有理Betti数被用B$ B$ -蛇来描述。本文用B$ B$ -蛇明确地描述了B$ B$实复面体型上同环的乘法结构。

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