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arXiv · 2604.27874

On the homotopy types of $4$-dimensional toric orbifolds

Tyrone Cutler·Tseleung So
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Abstract

The cohomological rigidity problem for toric orbifolds asks when an integral cohomology isomorphism implies a homotopy equivalence. In this paper we reformulate the cohomological rigidity problem in the context of $4$-dimensional toric orbifolds by introducing what we call proper isomorphisms, a variant of a concept studied by J.H.C. Whitehead. We prove that each proper isomorphism class of $4$-dimensional toric orbifolds contains at most two distinct homotopy types, and that the two classifications agree in certain special circumstances.

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Tyrone Cutler, Tseleung So. 2026-04-30. On the homotopy types of $4$-dimensional toric orbifolds. https://arxiv.org/abs/2604.27874

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