 Abstract : There are several advantages to studying a topological space whose integral cohomology groups are concentrated in even degrees and torsion free. For instance, their K-theory and complex cobordism groups may be deduced immediately, because Atiyah-Hirzebruch spectral sequence degenerates. It is well-known that the cohomology ring of a smooth toric variety satisfies this property, however there exist singular toric varieties whose odd degree cohomology groups survive. Hence, it is natural to ask a sufficient or necessary condition for vanishing odd degree and torsion freeness of cohomology groups of a toric orbifold. In this talk, we introduce some partial results about this question. This is a joint work with A. Bahri and S. Sarkar. |
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