Realizable Cohomology Classes of Dihedral and Generalized Quaternion Groups

Sutirtha Datta; Jyotirmoy Ganguly; Rohit Joshi

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arXiv · 2610.32680

Realizable Cohomology Classes of Dihedral and Generalized Quaternion Groups

Sutirtha Datta·Jyotirmoy Ganguly·Rohit Joshi

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Abstract

We compute the Chern classes of irreducible representations for the dihedral groups $D_{2n}$ and the generalized quaternion groups $Q_{2^n}$. Utilizing these computations, we investigate whether every even-dimensional class in the integral group cohomology of these families can be realized as a Chern class of some complex representation. It turns out that this realizability question answers in the affirmative for the generalized quaternion groups. In contrast, it turns out that the answer for dihedral groups is erratic.

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Sutirtha Datta, Jyotirmoy Ganguly, Rohit Joshi. 2026-10-23. Realizable Cohomology Classes of Dihedral and Generalized Quaternion Groups. https://arxiv.org/abs/2610.32680

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