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October 3, 2025Open Access

On the integral cohomology of real toric manifolds

Key Points

Integral cohomology groups are calculated using combinatorial data from simplicial fans.
A combinatorial formula characterizes the ring structure modulo elements of order 2.
A criterion is established for determining when a real toric manifold is spin^c.
These findings generalize prior work by Cai and Choi, enhancing mathematical understanding.

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 spinᶜ.

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Cite This Study

Feifei Fan (Sun,) studied this question.

synapsesocial.com/papers/68e02f3cf0e39f13e7fa26ce https://doi.org/https://doi.org/10.48550/arxiv.2509.06059

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