On the integral cohomology of real toric manifolds

2025/09/07 by Feifei Fan, Fan, Feifei
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Topological and Geometric Data Analysis #Commutative Algebra and Its Applications

paper · pdf · doi:10.48550/arxiv.2509.06059

Abstract

Real toric manifolds are the real loci of nonsingular complete toric varieties. In this paper, we calculate the integral cohomology groups of real toric manifolds in terms of the combinatorial data contained in the underlying simplicial fans, generalizing a formula due to Cai and Choi. We also present a combinatorial formula to describe the ring structure, modulo the ideal consisting of elements of order 2. As an application, a combinatorial-algebraic criterion is established for when a real toric manifold is spin^c.

Citations

• Cohomological rigidity of manifolds with torus actions: I
• Multiplication structure of the cohomology ring of real toric spaces
• Integral cohomology groups of real toric manifolds and small covers
• Thirty-five years and counting
• On products in a real moment-angle manifold
• On the cohomology and their torsion of real toric objects
• Derived subdivisions make every PL sphere polytopal

Related

• On the cohomology and their torsion of real toric objects
• Multiplication structure of the cohomology ring of real toric spaces
• Real Toric Varieties: Interactions between their Geometry and their Topology
• Morphic cohomology of toric varieties
• Combinatorial generators for the cohomology of toric arrangements