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arXiv · 2604.27984

The transverse singular complex

Greg Friedman·Anibal M. Medina-Mardones·Dev Sinha
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Abstract

Let $M$ be a smooth manifold without boundary and let $\mathcal{T}$ be a countable collection of manifolds with corners, each equipped with a smooth map to $M$. We show that the singular simplicial set $\mathrm{Sing}(M)$ of $M$ deformation retracts onto the simplicial subset $\mathrm{Sing}^{\mathcal{T}}\!(M)$ of smooth singular simplices that are transverse to every element of $\mathcal{T}$.

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Greg Friedman, Anibal M. Medina-Mardones, Dev Sinha. 2026-04-30. The transverse singular complex. https://arxiv.org/abs/2604.27984

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