Invariant and Coinvariant Morse Homologies for Orbifolds

Erkao Bao; Lina Liu

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arXiv · 2511.17811

Invariant and Coinvariant Morse Homologies for Orbifolds

Erkao Bao·Lina Liu

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Abstract

In this note, we construct invariant and coinvariant Morse chain complexes with integer coefficients for any compact effective orbifold. We show that the homologies of these two chain complexes are invariants of the orbifold. We conjecture that the homology of the coinvariant chain complex computes the singular homology of the underlying topological space with $\mathbb{Z}$-coefficients, thereby refining the construction by Cho-Hong, which recovers the homology over $\mathbb{Q}$. In contrast, the homology of the invariant Morse chain complex is sensitive to the orbifold structure.

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Erkao Bao, Lina Liu. 2025-11-21. Invariant and Coinvariant Morse Homologies for Orbifolds. https://arxiv.org/abs/2511.17811

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